Might be obvious for the seasoned, might not be for the beginner, but I don’t think it’s been mentioned here:
Your soil returning to the hole (backfill) should be compacted periodically. Add a layer, compact, add a layer, compact. This secures the soil around the roots and prevents the tree from tipping over in the wind. It also prevents your soil around the tree from sinking to create a depression over time (loose soil settles over time) which would need to be filled in to avoid puddling as well as destabilizing the tree.
I usually do 3 layers of filling and compacting, depending on the size of the hole. The top layer starts off over-filled, but after compacting ends up being level with the surrounding soil (err on the side of slightly higher, but AVOID the “tree volcano”—image search if needed).
I’ve used a wood garden stake (1”x1”) with success but anything similar size would work. Tamping with “medium” strength (not too hard, not too soft). Avoid hitting the roots.
Another reason this helps is because, as the tree roots will have consistent soil density to move through. If the soil is loose right around the tree and compacted further out (where you didn’t dig), the roots may tend to stay in the looser, softer soil rather than extending into the undisturbed soil beyond the hole.
Last tip (which may be controversial) is to add your soil amendments (compost, etc.) AFTER you backfill the hole with the original soil only. Sprinkle your amendment in a circle that is wider than the hole you dug so it’s sitting on top of the original soil. Rain water (or irrigation) will carry the nutrients down into the soil and the tree roots will grow outward and out of the hole into the original soil. Adding lots of fluffy compost to the hole can compromise soil stability.
As you may realize, these methods are intended to encourage stability. Soil can be amended over time (from the surface), but if the tree falls over, what’s the point? I planted hundreds of trees at orchards and working for arborists using this method. As long as the trees aren’t very large when transplanted, no stakes are necessary.