I won't address the issue of whether silver bullets actually existed; that said, they actually do exist: the Northwest Territorial Mint produces them as a novelty (although they represent very expensive ordinance!).

There are a number of ways to approach the question of silver, bullets, and metals in general when it comes to the supernatural. The idea of a silver bullet is linked, intrinsically, to the invention of firearms, so it is clear that the motif does not have terrible deep roots, at least in the form of bullets. The online etymological dictionary suggests a possible earliest reference to the term as appearing in 1808. Silver bullets were made famous in the twentieth century by werewolf films and by the Lone Ranger (who used silver bullets against less supernatural opponents). There is limited evidence of silver bullets occurring in actual oral tradition. The heroes of "The Two Brothers" in the nineteenth-century collection of the Brothers Grimm shoot silver buttons stuffed in a blunderbuss as an effective weapon against a witch. In the gigantic Motif Index of Stith Thompson, there are only minor references to silver - and only one, really, for a silver bullet: D1385.4 Silver bullet protects against giants, ghosts, and witches. In short, the motif of the silver bullet is more at home in twentieth-century media than it is in earlier folk tradition.

Then there is the question of metals as being effective against supernatural agents. In general in Europe, the go-to metal was iron, a substance that protected people from all kinds of threats. Silver by analogy as a heavy steel-colored metal was naturally drawn into this orbit, but iron/steel would always be the preferred metal because it was accessible and most folk belief reinforced its use far more than any other metal. The idea that silver was an effective device being ancient is embedded in a matter of cherry picking sources. This site, for example, traces the efficacy of silver to Ancient Greece and it provides other examples scattered across time to suggest that this theme crops up here and there. The evidence here is slim, however, and the scarcity of references underscores how this was not the metal of choice. If this discussion were about historical references to iron and steel as effective against the supernatural the challenge would not be to find references, but rather, the task would be finding the best examples to demonstrate the point among the hundreds of thousands of references.