The slutty, slutty part of me wishes this was a real thing, but like... there is an objective answer to this. It's been studied to death, and the answer is no. It's impossible to fit 50% of the world into only two personality types, and behavior is much more the result of social conditioning than anything innate. So with men, we see populations molding to whatever that society has conditioned men to believe is culturally "male" in that society, and it changes with time.
Aggression = Male is a relatively new thing. Victorian gentlemen would be AGHAST at us placing such importance on fisticuffs.
Crying = Feminine is so new that there exist movies that show a zeitgeist where the exact opposite was true. Until REALLY recently, like the 1970s level recently, crying was a manly thing to do. Sparacus cries, Gilgimesh cries, dude in old war movies cry.
So... personality is largely based on culture- there just aren't any innate traits to pick out. And I'm not honestly sure what the "alpha" and "beta" thing is all about- in my head an "Alpha" is the jock dudebro and the "Beta" is the nerdy kid- but like... the nerds watched DBZ and found out that you could get ripped and then go play video games about it. The culture changed in such a way that "nerd" shit became mainstream, and we've got guys who get ripped as shit for their 300 cosplay. Because of that, of how in-flux this thing is, there's no way to classify all men into two categories, and when classification is impossible and overlap is such that a ven diagram would be a circle- then it's just not a real thing.
Having said that, if we assign the term "Alpha" to "having leadership qualities" and "Beta" to "Being good in group dynamics and shying away from leadership"- and also drop the gendered notion, then that IS a real thing, and it's largely focused on a psychological concept called Locus of Control that IS innate and genetic, and can be observed as early as three months. But I'm almost positive that that's not what you're talking about and there are 5 levels, not 2, and they're pretty fluid based on things like current mood, developmental level, and emotional intelligence.