Lament of Innocence
Chronologically, this game comes first in the "main" series (as opposed to the Lords of Shadow reboot continuity) and concerns itself with explaining the rise of the Belmont clan. Leon Belmont, hero of the Crusades (the game conveniently ignores the fact that the West never really won any of the Crusades, at least not for very long) has come back home to the woman he loves (with every intent of marrying her).
Sadly, things aren't going to go so well for Leon. His woman, Sara, is taken by the Vampire Walter Bernhard (they were early times, when a man could use the title "Vampire" and not immediately have a stake thrust through his chest). Leon storms to Walter's castle to defeat the goddamned bathead (okay, we swear we won't use that joke again) and save his beloved.
Well, really, he's able to do one of two items on his to-do list, and while he fails to save Sara, she does give up her life to give Leon the power to defeat Walter.
From this point forward Leon declares that the Belmonts will always exist to defeat the vampires.
It's important to note that Dracula never actually appears in this game. Walter has a moveset very similar to Dracula, bestowed upon him by the Ebony Stone (a magical mulligan mentioned only this once in the series and never seen again).
As it so happens, Matthias Cronquist, a supposed friend of Leon, was actually behind the whole adventure, manipulating Leon and Walter into a battle so that Matthias could use the Crimson Stone (a counterpart to the ebony mulligan) to steal Walter's powers upon the vampire's death.
This last bit is important, as the implication is that Matthias, by way of the Ebony and Crimson stones, becomes the vampire we eventually know as Dracula. To say it again, in this game Matthias actually is Dracula and will one day take on the history and name of Vlad Dracula.
While we at The Inverted Dungeon would never tell Konami how to write their games (at least not to their faces, as they refuse to accept our meeting requests), we will point out that the likelihood of this Matthias Cronquist actually being Dracula is absurdly remote. Dracula, as so many of us know, is based on a real person (Vlad Dracula, aka Vlad Tepes). He is one of the most well known, well researched figures in history, and for someone else to just "be" him is so unlikely as to be considered completely impossible and truly absurd.
The only explanation is that, somehow, Matthias was out in the world and ran into Vlad Dracula. Somehow he was able to steal Vlad's identity and eventually become Dracula, all without anyone who actually knew Dracula asking anything about it.
It's even less likely that he just took the moniker "Vlad Dracula" without there ever actually being a real Vlad Dracula to begin with. Among all the other reasons we could come up with, the one that stands out most of all is that Vlad Dracula is the son of Vlad Dracul -- it's in his name. Dracula means, literally, "Son of Dracul", the "a" at the end implying "son of".
To note, Matthias actually is also based on a real person (Matyas Corvinus, who also did actually have political dealings with Dracula), so trying to reconcile all these weird histories and facts together is difficult (did we already say impossible?). Allegedly Konami was, at one point, working on a game that would explain this better, but so far they have not released any game set around the necessary time period. Presumably they threw their hands up in the air and collectively said "screw it" to the whole idea.