Figs are a really easy subject for cuttings so you’re in luck. I took cuttings from my FIL’s tree after he died. Easy. Root in a soil mix, not water. Here’s a handy link https://www.bbc.co.uk/programmes/p08t6bdl. Take a bunch to increase your chances.

Thanks so much, that was very helpful. I’m getting a couple blocks of coconut coir to plant a dozen blueberries instead of peat, so I can use my leftovers for propagating mix. He didn’t touch on what moisture level these should stay at though. Should I keep it moist or let it dry out a little in between watering to avoid mold or rot? So I assume when you start seeing new leaves form there’s enough root growth in order to transplant it into proper soil for nutrition? I just don’t want to be plucking it out of the pot every couple months peaking for roots, but I don’t want to starve them either if they start rooting and I don’t realize it.

Spread your risk by trying different methods. An easy way to root is plant Dormant cutting directly in ground after last frost. parafilm on exposed end will help

Do not assume that leaves mean roots. New leaves often appear long before any roots have formed. I started mine in ordinary potting mix and they stayed there for months. I didn’t water them at all for weeks after the initial wetting. They were under plastic bags and didn't lose much moisture.

I've seen hardwood cuttings inserted into loose soil outdoors, without coverings during February recommended on the web in the past as a good basic method for getting figs started. Of course, you might not have time to wait until then in this particular situation.

I did mine in pots under plastic bags but they were left outdoors as it was summer. At this time of year I’d probably do them inside with some bottom heat if possible. However, if you can get a good number of cuttings you could try a variety of techniques.