This might work, but check with the DM
What constitutes an unoccupied space is not that well defined, the rules only talk about space in relation to what a creature controls. Going by that, any space that is not controlled by another creature is unoccupied, and that would include spaces above the ground.
From a balance perspective, being able to deal an extra 3d6 damage per turn and possibly inflict the prone condition as a bonus action is strong - not only does it give you an automatic use for your bonus action, it also deals considerable extra damage, it also reduces the creatures movement by half for needing to stand, unlocks tactical options from clearing movement paths, and other characters are able to attack with advantage until the creature can stand up again, which can translate into even more damage.
Caveats
The combat rules in 5e are are mostly written as if you operate on a 2D plane, not really considering the 3D-aspect of combat. For example, the rules for space in the PHB (p. 191) are only talking about 2D-areas creatures occupy as space, like 5 x 5 feet, not about 3D volumes. The DMG on page 250 says
You can draw tactical maps with colored markers on a wet-erase vinyl mat with 1-inch squares, on a large sheet of paper, or on a similar flat surface.
And the intro of Mighty Impel says
Your connection to giant strength allows you to hurl both allies and enemies on the battlefield.
"On the battlefield" might imply that you cannot hurl them avove the battlefield, and when the ability talks about falling, the idea might be that you can move a creature over a chasm, off a platform etc. not that you throw it up into the air.
Because throwing up would be powerful, and because it deals with an aspect of position in combat that is not well covered by the rules, I'd check with the DM how they interpret this: are they OK with throwing up, or are they ruling you can only move them over the mat, and need a pit or something to drop them into. Best do so before game so you do not find out in a tense combat situation. If you are the DM yourself, you have to decide what you think makes for a better game.