You can simulate¹ falling down² by raycasting down like in quellenform's answer, but then taking the lowest ray for each group (not island, because one Suzanne is 3 islands), and displacing by that much…
An Animated Plane as a Base:
The Snapping Action:
¹ - not a simulation zone, "simulating" means "pretending"
² - well, not the process, just the end result