I don't use the word "Alpha" as a serious concept. It's a dumb word as used in the Manosphere and most of those who use it don't even know what it means. It comes from the study of canines and it means one thing, and one thing only: parent wolves. If you transfer it to humans, what you get is a patriarch.
Worse, the accepted definition in the Manosphere is an almost clinical definition of a narcissist, and there is nothing good about being a narcissist at all. Whoever came up with that definition has some problems, and I'd say some pretty deep-seated ones.
There are other problems. When you have a fantasy hierarchy of from Alpha to Omega, the wimps are going to call themselves Alphas (the wimp Ted Nugent is a perfect example) and sneer at and denigrate others as Betas, Gammas, Omegas, etc.
There is nothing new in the Manosphere, contrary to the delusions of the uneducated. Thinkers in the past discussed these things and they were just as smart as us, if not smarter. Personally I think they were smarter.
I recently ran across a book called Engineering the Alpha. The authors were smart enough to dismiss the accepted definition of "Alpha" and instead substituted another one, which is the best definition: the real Alpha is the most evolved you can be.
Guess what? I've been saying that for a long time, and it wasn't me who came up with the definition. It was the Greeks, well over 2000 years ago. More like 2200 years, as best as I can tell.
The Greeks believed you achieved eudaimonia (well-being/flourishing) through arete - which is excellence. Being the best you can be. Being the most evolved you can be.
"Excellence" is sometimes translated as "virtue," however, "virtue" means "the powers of man." Being the best you can be is a power inherent in all men.
Vince Lombardi (1913-1970), that most winning of coaches, had this to say about excellence: "The quality of a person’s life is in direct proportion to their commitment to excellence, regardless of their chosen field of endeavor."
Sometimes virtue is translated as "phronesis", which means "practical or ethical wisdom". Eudaimonia was (based on older Greek tradition) used as the term for the highest human good, and so it is the aim of practical philosophy, including ethics and political philosophy.
In other words, society and culture should be set up to allow people to be the best they can be.
The word "education" literally means "to draw out." Education is supposed to draw out what is already in you, and help you develop it to its fullest. What passes for education these days mostly does not do that.
The only way people can be the best they can be is through liberty - free from the depredations of the State. The State wants you to serve it. It's supposed to serve you, instead.
The State is a machine and wants to make you into a cog. Cogs can never develop themselves to their fullest potential. Cogs don't have any potential. They are what they are and that's it.
As Joseph Campbell put it, “Man should not be in the service of society, society should be in the service of man. When man is in the service of society, you have a monster state, and that's what is threatening the world at this minute...is the machine going to crush humanity or serve humanity? Humanity comes not from the machine but from the heart."
Lombardi also spoke of "the heart": "Once a man has made a commitment to a way of life, he puts the greatest strength in the world behind him. It’s something we call heart power. Once a man has made this commitment, nothing will stop him short of success."
What everyone wants is the richest and happiest life they can have. And by "richest" I mean internally rich. And by happiest I am the greatest well-being/flourishing you an possibly get. To be free.
You might even say the purpose of life is to express yourself to your fullest potential.