What did a full grown beard serve as for our ancestors?

I don’t know the answer, but it is possible the main purpose was to attract females. I also think hair generally is there to protect. Could be parasites or could be from the sun.

The vikings used to braid their beards to protect their necks and if long enough the upper chest in battle. Considering many of them went into battle naked it kind of was their only defense.

Sexual Dimorphism. Think of it as an arms race to be more “Male” and to be more “Female” in order to attract mates.

Long haired women yield men with male pattern baldness.

Here is a very brief article on the topic.

genetically everything that comes from us physically serves a purpose.

They don’t have to serve a purpose. A neutral trait which does not help or hinder reproduction can persist. Sorry to split hairs (lol) but I just wanted to mention it.

Anyway, I am very curious to hear more answers.

Er, warmth . . .

Yeah. Warmth. That seems like an obvious one that didn’t occur to me.

For breeding females to distinguish the men from the boys.

A scent trap? Having the scent of food on your person would be attractive in prehistoric humans. That would signal he is a good provider of food, and would provide proof of the type and quality of food he can secure.
It would also signal sexual maturity and physical health and vigor. In fact, it still does!
I like the answer about it being protection for the throat.
I don’t know what you meant by protection from insects. Human hair is attractive to lice, fleas, and other buggy vermin.

To attract females. And, as @Jewel said, it is a scent trap, but not for food. It holds the scent of pheromones close, bringing a woman who is attracted by those pheromones close to the man.

What @wundayatta says about trapping scent is true. This is why we get so much hair where we sweat, top of the head- armpits and crotch. I’m sure at a level, physical health and sexual viability can be smelled.

Speaking neolithic or earlier here, plenty of bugs to eat, right close to the mouth.
After that, fashion, or projection of wisdom of age.

I figure it was a handy paleolithic napkin.

Protection from the sun, wind, and dust.
I’m sure there’s a social aspect too.

It served as a place to store food for later consumption.

A sexual characteristic. It says male with a capital M.

Maybe to signal the females that “the male is ripe for reproduction” (He has reached puberty).

For those who have proposed a use, would this beard fit the needs?

It also allowed the Romans to pick out the barbarians with ease.
note Google content farming monitors, this means you PANDA:
Barba means “beard” in Latin, and when the Romans called hirsute foreigners barbarians they were strictly calling them “bearded men,” though the word shortly came to mean, rightly or wrongly, “rude, uncivilized people.” http://laudatortemporisacti.blogspot.com/2004/09/barbarians-and-beards_08.html

I think the same thing about pubic hair, seems useless and gross.