I would plant fast growing trees. You don't need to plant them tight against each other, but stagger them a bit and do some under planting. I would do it inside the fence (which I love, BTW) so you can tend to it.

I planted these trees as a boundary marker. They are gorgeous Japanese pines that grow like a weed.

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Sorry, but those are not Japanese pines......they are not even pines. Look much more like spruces and are not considered particularly fast growing.

Unfortunately, the time to plant for privacy screening is about a good 5 years before you need it. It is tricky to find something that will grow fast enough or that you can purchase large enough to provide much of a screen before that time frame. And fast growing conifers (evergreens) generally take up a lot of real estate so can infringe on the available yard space. Fast growing deciduous trees often get to be very tall and tend to have a lot of structural issues that make them less long lived or as desirable than slower growing (and smaller/shorter) species.

A mix of faster growing shrubs and few taller trees could work but there are few broadleaved evergreen shrubs suited for your climate. Do you still want or need the privacy in the winter as well?

I'd leave the fence and plant clumping (not running) bamboo on the other side.

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Who owns the property that immediately abuts your yard? Is it HOA or homeowners? There would be obvious advantages to you if you could install privacy screening at the TOP of the hill. In the first place, it gives the plants a height advantage. Secondly, it doesn't consume your yard space. Screening plants can occupy a large area of ground space relative to their height. While you'll want some large trees in the mix, the bulk of screening from other homes will likely come from large shrubs (15' - 20') which retain their foliage to the ground.

I would move the fence to the boundary line to start with

Move the fence it makes no sense to have the fence inside the property . What happens to the piece outside the fence, if it is your property than use it. As for privacy that will depend on what the HOA allows if you have an HOA. Because the house behind is higher than yours it will be best for you to plant taller growing shrubs or trees on that little rise too. Go to your garden center and ask what will work best where you are. I live in the same growing zone as you and have found that a mix of plantings bot tall and short is nice way to provide some privacy but of course no HOA to contend with.

I planted fast growing spruce trees along the street side of our property. Within a few years they were already providing almost complete privacy from the street.

Whatever you do,please plant your trees and/or shrubs with their mature size in mind. That way the plants will do well and look best.And do go to a local nursery for info and suggestions as to what thrives in your environment.

Move the fence for sure. In terms of what to plant it’s true you need time. We are one year into our garden and I feel for you as I wish it were bigger and fuller but you also adjust to what you have and in time it will be glorious.

Good for your zone - Arborvitae are native. Clumping some different sizes (giant, emerald, spire, etc) in a natural formation would be nice. Native holly also gets big. Square holes are better than round for sturdy roots. Check with Miss Utility before digging.