It should be possible, as long as the object you choose is located outside the antimagic field.
Targeted Effects. Spells and other magical effects, such as
majic missile and charm person, that target a creature or an object in the sphere have no effect on that target.
Catapult spell is instantaneous, the only magic is used on the object to launch it in chosen direction. It is not concentration sustained as telekinesis. According to the description, the projectile stops if it impacts against a solid surface. It is not a magical effect but pure physical force.
Still, if the caster would be able to cast 8th-leveI abjuration spell, a simple wall of force in a shape of dome, located just outside the antimagic field.
The answer from Wizards of the coast:
Thank you for contacting Wizards of the Coast. As long as the spell is within the weight limits. The spell is not a continuous spell it is a one time spell that launches a object. If you have any questions or concerns please feel free to contact us again at your earliest convenience.