Emulation Pokemon Fire Red/Leaf Green – Do Non-Kanto Pokemon Evolve Before Getting National Dex in Randomized Fire Red?

There is no known way of obtaining Mew within FireRed or LeafGreen, outside of messing with the save data / memory / ROM yourself (i.e., cheating/hacking) or getting it by trading (i.e., an event). There are no glitches that would enable a Mew encounter, either.

It depends on how you reset the game.

Most emulators offer what is called "save states". Save states contain the entire memory dump of a game, unlike regular save games which only contain what the developer believes is important for the game.

Save states are particularly popular among emulator users, because they offer a way to cheat, such as resetting a particular move in combat.

In this case, the save state will contain the RNG (Random Number Generator) which a regular save game would not; why keep the RNG in memory, if you can generate a new one every time you launch the game? Of course, this also means you cannot simply load a save state to improve your chances of getting a shiny Pokémon, you'll have to reload a regular save game instead.

In other words: you'll have to quit the game, launch it again, then load the save game from within the in-game menu.