Currently, we only know of three ways to become an alpha.
The first, and most common, is to defeat (kill) an alpha. Deaton implied that this was fairly standard when he explained what a "true alpha" was to Scott.
The second and more rare is to become a "true alpha" by force of will.
It is also possible, but unclear how, alpha status may be inherited.
Because you can't kill an alpha if none already exist, nor can you earn alpha status through lineage, we can deduce that the first alphas became alphas independently, without needing to take or inherit the power from an established alpha. Simply, someone had to become an alpha before that status could be passed down.
This means that one of two things must be true:
1.) "True alphas" are the original alphas, and the status of all other alphas has been either inherited or taken by force.
2.) There is a fourth way to become an alpha, which is somehow different than a "true alpha," yet is still obtained without the need of an established alpha.
Due to the sheer ratio of "regular" alphas to "true alphas" (or other original alphas), that we have seen in Teen Wolf and the claim that Deaton made regarding the rarity of the "true alpha," we can assume that many "true alphas" (or other original alphas) have been killed, passing their power to the werewolves who defeated them.
I think one thing that makes sense is that werewolves became True Alphas, in the beginning, and then it was discovered that a beta could take that status by defeating the alpha. After that, challenges for alpha status would become increasingly common, until eventually, no True Alphas remained, and all alphas achieved that status by victory.
No, this is not canon...but it is really something that made sense to me.
This puts into question what the difference of power is between a "regular" alpha and a "true alpha" (or other original alpha), and whether or not it is worth putting stock in, but that is another argument altogether.
