If Mew existed before Mewtwo, why does Mewtwo come before Mew in the pokedex numbers?

With no confirmed sighting before Mewtwo was created, Pokémon researchers thought Mew may have been just a myth. Mewtwo's creation may have confirmed Mew's existence in a way.

I am surprised to hear anyone ask this, but I guess it makes sense. The franchise is decades old at this point, and even foundational knowledge of the series is unknown to fans who started with later games.

As others have alluded to in the thread, despite being the first Pokémon trademarked (points for anyone who can name the first one designed) Mew was not actually in the game code when it went gold, only mentioned in the lore and in reference to Mewtwo's creation.

One of the developers changed the code after the game had already been tested and approved to enable Mew to be downloaded. Quite risky at a time when there was no internet connectivity to allow patching if it broke the game. (Not that Red and Green weren't broken anyway.)

In universe, Mew is said to have only been a rumour, only confirmed to exist after Mewtwo had already been created using its DNA.