Methods such as the "fight storage" glitch from the original games still work to generate a wild Mew battle, but Pokemon Bank is wise to that and knows that Mew isn't normally supposed to exist in the game. It will refuse to transfer a Mew from RBY unless its OT name is exactly "GF" and its ID No. is exactly 22796, which correspond to the details of the one Mew giveaway they ran that was compatible with the VC version of the game.
It's possible to forge the details of a Mew, or indeed any other Pokemon, after the fact to make it look valid and allow it to pass into Bank, but it requires a more sophisticated in-game (or possibly out-of-game) hacking method, and if you're using the freedom granted by that, you can create anything you want without regard for legality anyway.
