As Written no FlyBy, but hold on.
As mentioned, the rules as written do not support your neat idea, due to their simplistic nature: as soon as you enter a gravity field, you fall straight "down", up to 500 ft. per round if using Xanathar's rules, unless you have a Fly speed.
If you have access to flight, you could use. Even the most restrictive options -- a Fly Speed only on your turn, a few turns/day -- would be sufficient for your stunt.
A Glide ability, such as the Hadozee's, allows a character to move horizontally while falling. Depending on how much movement Glide allows, it could get tricky, but with a high enough Int your character should be able to compute a trajectory that allows them to exit the bubble by Gliding.
I shall note that your character could execute a FlyBy by staying outside of the bubble of gravity altogether, and throwing things in. The things thrown, once caught in the bubble of gravity, would fall towards the center.
Your DM would have to work out the effect on targeting; but for carpet-bombing precision may not be that much of a problem.
As Written no Carpet-Bomb, but hold on.
A larger issue with your plan is the idea of carpet-bombing. D&D 5.0 only offers limited Object Interactions.
For example, the rules for Caltrops mention:
As an action, you can spread a bag of caltrops to cover a square area that is 5 feet on a side.
So, 5 ft. x 5 ft. area per turn.
Rules for throwing vials of acid, etc... tend to have similar wording, and you only have 1 Object Interaction (as Free Action) on top to drop an object (if within the bubble of gravity).
If several characters do the fly-by, they can each throw / drop an object.
There are many spells with an area of effects, and some objects too. If you want a large area of effect, I'd advise into looking into those. Fireball, whether innate, by wand, or by scroll, would "carpet bomb" a large area.