If a fellow adventurer gets turned into a beast using the Polymorph spell can you administer first aid using a Health Potion?
If they retain the ability to ingest things and didn't drop to 0hp, you can.
@JeremyECrawford confirmed that you can administer potions to willing (or incapacitated, i.e. unable to consent or refuse) characters.
Assuming you simply wish to raise their health in their polymorphed shape you should be golden. As long as you have an action to spend on feeding the potion to your buddy and they have the ability to drink it (RAW potions explicity require being consumed to function).
If you want to administer a potion right when they hit 0hp in their polymorphed state, it wouldn't.
The transformation lasts for the Duration, or until the target drops to 0 hit points or dies.
Dropping to zero instantly reverts the polymorphed creature back to what it was. As such, if you get to ready your action you could use it to feed your fellow adventurer the instant a dangerous enemy tries to strike them, much like the way Catapult is used in this question.