The alpha male always

What makes you think that "alpha males" were the norm in the paleolithic?

always had more resources

I could probably be convinced that some individuals had more social capital than others.

What do you even mean by "had"? It seems extremely unlikely that in the paleolithic they had a concept of ownership even roughly like what modern capitalist systems employ. I'm quite certain they didn't think of land ownership the same way we do today. I'd doubt they thought of ownership of tools or food or clothing the same way we do either.

I'd imagine anyone who carried more stuff on their backs than they needed would have significant disadvantages (encumberance) compared to other folks.

This was a thing before civilization.

How do you know?

Just from looking at Wikipedia, I found a paragraph that starts "some sources claim that most Middle and Upper Paleolithic societies were possibly fundamentally egalitarian." (And that sentence has 4 citations.) It seems like the jury is still out at best on that topic.

And lets be honest, if we had more, would we really share it? Most people want more but when we get more, we do not divide it with others in our community. Very few give up their time and money for charity.

And what if that has a lot more to do with our modern world than with human nature?

Indigenous peoples in what is now the pacific northwest of the U.S. and Canada had rituals called "potlatch" in which the most wealthy would give away lots of their resources to those with less. Don't get me wrong, those folks were not paleolithic hunter gatherers, but they're a counterexample to your implication that humans with more never give things away to humans with less. And it was done regularly. (On occasions of births, deaths, adoptions, weddings, and other such events.)

Another example of this is the Moka ritualized exchange by indigenous peoples in in Papua New Guinea.