From what I could tell, it wasn't so much a "there can only be X number of accepted applicants," it's "there's a bar of expectations we expect junior knights to pass, if you're not there yet then nobody's gonna let you in."

That Sekke guy ("Zeke the Bronze") got absolutely bodied by Asta in the spar, and wasn't anywhere close to Yuno in terms of power, but still got picked by the Green Mantis squad. Meanwhile, Yuno himself had the approval of every captain so he got his free pick of who to join. Essentially, it depends on the standards of the captains themselves and whether or not they think someone qualifies after they've seen what that person's capable of.

Also, Asta wasn't the [i]only[/i] newbie--Noelle was stated to be a new recruit from the same batch. It's just that nobody wanted to be on the Black Bulls even if Yami raised his hand, cause, before Asta joined up, they were too dysfunctional. They were at -30 Stars for their missions because of their screw ups, lol.