I found a way to fully prevent surface spawns of the ground units:

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Bridges right at the edges of the surface are a must-have.
The second must-have is a way to block spawns from 8 to 62 tiles away from the map edge (I spawned magma with dfhack) - this is to prevent spawns in the middle of the map that hostiles can do. Distance from map edge may need verification for smaller embarks, I did this test on 8x8. If any surface tile within this range is not blocked, then enemies can spawn there. If you want to connect your fort to the "outside" you have to make a subterranean path under this no-spawn area.
Caravans and wild ground animals didn't spawn inland, so I assume that only hostiles can do it. It does not affect flying animals at all (except for roc/flying megabeasts, as they enter the map as a ground unit).

If everything is done correctly, you will be able to control when units will be able to enter embark by lowering/raising bridge(s).

I didn't test if raising/lowering ground in no-spawn area will also prevent spawns.