Each of the oldest and latest Ravenloft publications name Strahd...
As Dan O’Shea’s fine answer details, the original 1983 adventure Ravenloft gives Strahd the epithet “The First Vampyr” in his statblock. The only other pre-5e mention of this claim, however, is the table of contents from the same Ravenloft adventure, which, as Daniel R. Collins’s answer shows, isn’t actually used on the corresponding page in the text—suggesting that at some point, the title of the section was updated and the table of contents wasn’t. It’s not clear how strongly Ravenloft was ever asserting that Strahd actually was the first vampire—none of the actual text discussing Strahd makes that claim, just the epithet.
As noted in the question, the 5e Van Richten’s Guide to Ravenloft then repeats this claim, and in fact doubles down on it, asserting it is more than an epithet but a fact, and that it applies to the entire multiverse.
...but everything in between names Kanchelsis
In between Ravenloft and Van Richten’s Guide to Ravenloft, Ravenloft publications have avoided, or even outright rejected, this claim, as we can see in Kirt’s answer with I, Strahd—The Memoirs of a Vampire and Dan O’Shea’s answer with Expedition to Castle Ravenloft. So literally the very first Ravenloft publication, and the very latest Ravenloft publication, are the only ones to claim Strahd is the first vampire. That’s nearly forty years of not making that claim.
And in between, we have a different character that is claimed to be the first vampire.
Monster Mythology (AD&D, 1992) describes Kanchelsis, vampire god of blood, and says
His origins in myth are shrouded in secrecy, but the avatar often takes half-elven form and travels with an elven or half-elven vampiric companion, so the dreadful secret of the Seldarine may indeed be a truth.
(Monster Mythology, pg. 112)
The “dreadful secret of the Seldarine” mentioned here is not described in greater detail in this entry, nor is it described elsewhere in Monster Mythology (that I can tell; can’t Ctrl+F a book from 1992). But it seems clear that the reader was expected to be familiar with the story, and we can find more information about it from other sources:
The “Class Acts: Cleric—Forgotten Faiths” article in Dragon vol. 359 gives Kanchelsis stats for the “v.3.5 revised edition” of D&D (in its very last 3.5e issue), and goes into more detail about the “dreadful secret of the Seldarine.” Note that Dragon magazine was, at the time, published by Paizo under license from Wizards of the Coast—in this case, we reference it primarily because the author here knows what Monster Mythology was referring to, rather than as a primary source.
In the earliest days of creation, blood served as the paint with which the freshly inspired deities poured out their creative works. […] On one world, though, the works of the elven pantheon, the Seldarine, and a nameless creator of humans intruded upon one another. This accidental mixture of birthed a being possessed of the beauty and longevity of the elves, but with the hu[n]ger and ambition of humanity. More and less than both races, the thing became known as Kanchelsis, the first vampire, the darkest secret of the Seldarine.
(Dragon vol. 359, pg. 121)
Kanchelsis is extremely obscure, while Strahd is one of the most famous characters in D&D—one can see why Wizards of the Coast might prefer that a major title like this goes to the bigger character. But Dragon vol. 359 itself even mentions Strahd’s claim—another article in the same issue, listing the most famous villains in D&D, refers to him as “the so-called first vampire.”
Strahd as first vampire in the multiverse basically makes no sense
Strahd may well have been the first vampire in Barovia, or perhaps even in the unnamed world in which Barovia was situated. He may well have been sire to all of the other vampires in the country, which gives him some local claim to the title of “first.” But the original Ravenloft adventure wasn’t set in Greyhawk or the Forgotten Realms (which existed only in Ed Greenwood’s personal notes at the time) or the wider D&D multiverse (which Gygax had only begun to sketch out). It was stand-alone, which meant it could say whatever it wanted without concern for “D&D canon”—which, to a great extent, also didn’t exist at the time.
Strahd is also, arguably, the first vampire in the Demiplane of Dread—because he was arguably the first anything in the Demiplane of Dread. Barovia was the first Domain and Strahd was its first Darklord. The Dark Powers seem to have created the demiplane around him, or at least its initial creation was for him. The whole of Barovia was transported by the Mists from the Material Plane to the Demiplane of Dread, but even if any vampires in Barovia at the time would have simultaneous claim to being “first,” it seems pretty clear that Strahd’s claim is best and strongest—especially since, as we just discussed, he probably sired the others.
But in the wider multiverse, Strahd is a very, very unlikely figure to be the first vampire. Strahd isn’t from the mists before time or anything like that; he’s ancient, in the way vampires are ancient, but he isn’t ancient like the planes themselves are ancient. Kanchelsis, on the other hand, would be, dating back to the earliest days of mortal life being created by the gods. Considering how common vampires are throughout the planes—and considering the existence of blood fiends, who are literally “mortal fear of vampires”-incarnate—that’s the kind of age we should be looking at for vampirism’s origins. Moreover, for Strahd’s entire tenure as a vampire, Barovia has been nearly impossible to leave, so it’s just not possible that he is the ultimate source of vampirism. It’s just barely possible that Strahd could have been first, but then an independent strain of vampirism developed outside Barovia, unrelated to Strahd, but that is extremely implausible. Hence the 3e Expedition to Castle Ravenloft’s observation that “the claim seems unlikely.”
Beware the lore claims made in Van Richten’s. It does not treat existing D&D canon with care, and makes numerous claims that are outright nonsense, even with the extremely limited subset of D&D lore that has been published for 5e specifically. I would put this in that category, since it’s literally impossible for all vampires to trace their lineage back to Strahd (Barovian vampirism has never had an opportunity to spread to any other place or plane), and it’s nearly as impossible to imagine that there were no other vampires before Strahd.
