There are 2 main theories in my headcanon that I play around with:
1- 19th Century Nazi Soldier like @Cestus_II pretty much described.
The problem with this theory is that his Alpha body is too young looking to be his original body, and there is no indication that Bison developed cloning tech before Alpha 2. Prior to this technology, Bison likely jumped from host to host by sensing they are compatible, defeating them, then taking over (Kinda like what happened to Rose).
So the issue here is Bison’s alpha body has to be his original body. It holds his DNA which he used to create and mold all his “children” from. So either Bison looks much younger than he lets on in Alpha or he is actually just 40-50 years old then and Rose was his first body jump.
We can definitely interpret that he is attached to his original face/body in some fashion and always goes back to it when he is done with the in-between bodies. Like most Dictators in history, he likely has a vain and eccentric streak, so taking care of his looks and the image he projects out into the world is probably something he considers (hence the statues everywhere).
2- Bison is not a human being have a demonic experience, he is a demon having a human experience.
This theory plays with the idea that Bison is a devilish force of nature or became a devilish force of nature. This theory implies that Bison likely has no preferred sex or appearance, has had many throughout the ages, and it’s simply a coincidence that in the decade that the SF main story arc takes place, Bison happened to look the way he did. Probably out of convenience and practicality.
The sophistication of Shadaloo’s technology in 20th Century probably made his body jumping shtick a whole lot more accessible.
As out there as this theory sounds, it has a lot of basis in the canon. A lot of what Bison says in Alpha 3 especially alludes to him being beyond humanity and synonymous with Evil itself (Chun-Li, Vega, and Cammy endings spring to mind). His demeanor and attitude especially in SF5 show utter indifference and apathy to everything going on around him, the kind you would expect from someone or something not bound to rules or time.
The problem with this theory is that Bison has “DNA” or “clones” of him, implying that he has a human origin of some sort. Then again, if Bison is essentially the/a Devil, he could’ve faked his human origin. I doubt anyone in Shadaloo knows his truth if it were his truth. Only Rose might sense this, but not completely.
Whatever the case, I hope Capcom never really delves into his origin too deeply. Removing the mystique from villains ultimately ruins them, especially if it attempts to humanize them or give too much reason to their rhyme.