Yes, it will work. And you will have a fertile plot with a lot of decomposed organic material and healthy microorganisms, your microherd, that helped with decomposition, in your soil. It was the first step I did when starting my garden, although I did it the other way around, covering the area with tarp first, digging after. Your approach is probably better. Do it as soon as you can and keep the tarp as long as you can next year for the best results.

Agree with Kimmq, if you cover the part you are not going to tend this year with cardboard under 4+ inches of organic matter, it will be awesome and ready to use next year. Use thick corrugated cardboard overlapped at the seams generously. Remove any tape or staples. By this method, your soil is improved while you smother the current unwanted plants. The less you disturb it to plant next spring, the fewer buried seeds will be exposed.

When you are finished using the tended spot this year, you can cover it to get it ready for 2020. While you wait, you could sit pots in the area so it's not so bare.

One further point. It rather depends on what weeds you have. For example, I know from experience that cardboard will not smother bindweed, enchanter's nightshade or brambles.

I wonder if the previous respondents paid sufficient attention to
the circumstances described by OP.

First of all, starting a new garden in the area occupied by
established grass and weeds is very different from smothering a few
unwanted weeds in a flower bed. I fully agree that in the latter
scenario using cardboard covered with mulch could be good enough.

Second is the quite considerable size of the lot. Covering with
“thick corrugated cardboard overlapped at the seams generously”
(after previously removing any staples) an area 30x45' and putting on
top of that 4+ inches of organic matter (where to get such amount
of it from???) could be quite challenging task for anybody, but especially for a person in OP's situation, with a tiny child requiring almost constant attention,
who, as s/he writes, can keep up only with gardening a small area
30x15' (1/4 of the whole plot), and that's it. Looking for that
amount of cardboard and mulch, transporting it, spreading, in OP's
circumstances . . . Come on, let's be realistic!

Last, but not least, I did it with second-hand tarps (which I got
from the local sawmill), and it worked very well. It killed the
growth and seeds without exterminating my soil organisms. To the
contrary, the organic matter was well decomposed and the soil fertile
underneath, what could not happen without them.

I use Grass Killer spray from Walmart $.6 a bottle. It works well in my rose bed.

We are talking here about chemical free approach.

I speak from experience, from doing what I described many times in OH and AL, not just theorizing. Smothering does work. If one is trying to smother part of something that is connected to parts that are outside of the smother area, it could fail, like bindweed. Severing those ties with a shovel around the edges would fix that. Bindweed will perish under a smother, as I've seen, and I have also successfully smothered dewberry vines, smilax, bahiagrass and torpedo grass, Bermuda, St. Augustine, Canada thistle, Cannas, baby cherry laurel trees, Stachys floridana, spiderwort-type Tradescantias, and the new growth trying to come from stumps when trees are cut down, just off the top of my head. I can't think of any instance where a smother failed.

Large cardboard is easy to find at a furniture or appliance store, call and make arrangements. If one lives in an area where people bag leaves, gathering enough free OM to successfully smother anything is possible. One can buy mulch &/or compost by the bag or the truckload.

I don't own any chemicals and don't find them necessary to keep cultivated areas free of unwanted plants. A smother is a 1-and-done. No need to remove anything later. The few spots I've tried to garden without first smothering have ended up being exponentially more labor intensive in regard to pulling unwanted sprouts and time spent watering.

One either wants to garden or they don't. It doesn't just appear, there is work involved (or paying someone else to do it.) I am not a large or strong person, and I also have kids, a job, and other interests. If I can smother unwanted plants, anyone can.

My experience has been different, Tiffany. I have had my allotment for nearly thirty years and the soft fruit section has always been covered, after one through double digging at the start, by permeable landscape fabric for most of that time and by cardboard covered in several inches of woodchips or leaves for the last couple of years. Even with large sheets and carefully overlapping them bindweed will find the joins and weak spots. It has been controlled but not eradicated. Raspberries and enchanters nightshade have also continued to pierce the cardboard occasionally. Perhaps it's the climate which makes a difference. There is rarely any period of the year when there isn't ample water and cardboard becomes soft within a day or two of being laid down. I've never used chemicals either but I still have to patrol constantly for bindweed tendrils sneaking up through the covering. It is definitely not a one and done in my conditions. I have to replace the cardboard once or twice a year as it disintegrates so quickly. I'm trying the technique because I've read about it here on GW but I have to say I am in a minority. I know of no one else who does it. Perhaps it's just too labour intensive, finding the card and the mulch material, and doesn't work so well in a wet climate.

Like Tiffany I have numerous times made new planting beds simply by covering the grass and unwanted plant growth (weeds) with newspaper and then a mulch to hold the paper in place and hide it. No, that will not totally kill off some unwanted plant growth such as Ivy or other perennial, persistent plants, forever, but it will kill them off for this year. I have found the soil when this is done in better planting condition than when the bed was tilled although it may be 6 to 8 weeks before I could.

Many people seem to think that covering a planting bed with a mulch will totally eliminate unwanted plant growth and it will not. Mulches will aid in suppressing that unwanted plant growth. Plants such as Bindweed, Ivy, the bramble berries, Nightshade, etc. will grow where they wish and only diligent removal of the roots will stop them. Even many plant poisons are not all that effective at control of these.

We killed the grass (and weeds) on a 500 sq ft area last spring using cardboard and mulch, and thus far I haven't seen any re-emergence of either. However, to be fair, this area didn't contain too many of the deep rooted things like bindweed, etc. to begin with - just grass, dandelions, clover and creeping charlie, for the most part.

We had just moved and had a ton of cardboard boxes leftover, so we had plenty to put down a double layer of cardboard. We topped it with several inches of wood chip mulch (free from the city) and let it sit all spring and summer (about 6 months). In the fall we raked the mulch back to find everything dead, with most of the cardboard disintegrated as well. At that point we dug everything up, removing any deep roots we found along the way, but there really weren't many. We installed beds and filled them with the soil we had dug up, then mulched those and left them over the winter. No weeds have appeared as of yet this spring, and the beds that I planted with garlic, tulips and ramps are doing very well, so I'm guessing the soil is in great shape!

@ kimmq “I have numerous times made new planting beds simply by covering the grass and unwanted plant growth (weeds) with newspaper and then a mulch to hold the paper in place and hide it.”
Yes, I too made new planting beds in similar way, using simple cardboard and mulch, I don't use newspapers. But you are talking about planting beds here, not about a 1350 sq. ft. plot. And it makes a big difference!

@ Tiffany: It looks like, Tiffany, you are talking about completely abstract situation here. Breaking it down to the circumstances described by OP:

- I don't believe it is always so easy to find a furniture or appliance store reasonably close to where one lives (what distance seems reasonable to you?), where they have on hand at any given time 1350 (30 x 45) sq ft. (without overlapping, and much more than that when "overlapped at the seams generously") of thick corrugated cardboard.

- Supposing that yes, one has overcome the first obstacle successfully, now you have to bring all that stuff home. Not everybody has a truck necessary for transporting such amount of cardboard. I, for example, don't. So, what is your advice how to get it to your place?

Let's forget for now all those chemicals used to make corrugated cardboard boxes, although not everyone would want to have them in the garden!

- As for the leaves to use as mulch on top of the cardboard, who bag leaves at this time of year??? I will venture to say that getting any in April is practically impossible, not to mention 17 + + cubic yards of them!

- As for that other mulch and compost that “one can buy by the bag or the truckload”, it is in most cases far from being organic. Even if it is called as such, I would never put the stuff in my garden.

Anyhow, in OP's circumstances one would need, by easy calculation, 450 cubic feet (roughly 17 cubic yards) of it, even without that '+' you are talking about in your first post. An average commercial dump truck holds something between 10 to 14 cubic yards. So two trucks would be necessary to bring all that stuff to OP's place!

- Now, having all that thick corrugated cardboard and mulch successfully dumped at one's place, how much time and effort is needed to remove all that plastic tape and, as you propose, the staples from the 1350 + + sq ft. of cardboard, spread it “overlapping generously at the seams” (for overlapping you would need much more than 1350 sq.ft. of it) in the garden and cover it on top with 4” (or as you propose 4” +) of mulch?

- And what to do with all that cardboard and mulch after it fulfilled (?) its purpose of smothering the grass and weeds? Turn it over into the soil? Would not decomposition of such amount of OM take too much nitrogen from the soil? Plant in the mulch left on the surface? As far as my knowledge goes it is not always possible, it depends on what you want to grow, and not every gardener is experienced enough to do that successfully, anyhow.

When proposing all the above very time and effort consuming tasks you are clearly forgetting, Tiffany, what OP says about not having time for anything more than taking care of the relatively small garden plot!

Even biondanomina in the post above is talking about only 500 sq ft area (about 1/3 of the size of the area OP is talking about), and doesn't mention any manpower or time limitations!

On my way home from work every day I passed numerous sources of cardboard, it does not need to be a furniture or appliance sore although there were those just a bit off the route. Grocers, hardware stores, hundreds of places get product in cardboard boxes. I gave up, years ago, planting beds of a 30 x 45 size opting for 4 x 45 planting beds since they are much easier to maintain. If you consider that half of a 30 x 45 garden is wasted space (you need paths to walk on) a garden that big does not make much sense.

Obtaining leaves at this time of year is not impossible since many people are at work cleaning up winter debris and the wind has blown many leaves into yards that people think they need to get rid of. There will be some available, but planning ahead and making provisions last fall would have been better.

When I used cardboard I found no problem removing any tape, staples yes. There is no need to remove the cardboard once the grass and other unwanted plants are dead since the Soil Food Web will convert that into a soil amendment. Since we know today that tilling is bad for the soil why bother doing that? Since the cardboard and mulch material are on top of the soil the SFW digesting them will not cause a temporary tie up of soil Nitrogen as can happen if raw organic material is tilled in to the soil.

It took me several years to learn that one very large garden looked quite impressive but was a lot work and a planting bed 4 feet wide by however long I wanted was much less and while it may mean 3 or 4 of them they produced more in product than did the large garden where half the space was waste.