If you have a hex editor and are comfortable with Advance Map you can add it.
1. Open your hex editor and change the 97 at byte 0x1D402 to 00. This should make mew obey. (credit to colcolstyles)
2. There's an overworld mew sprite in A-Map, so you can set up a mew event wherever you like. I plan to do the cubone storyline earlier and put Mew in the ghost tower where Rockets have stashed it after nicking it from Silph Co.
However he is playing the game on a cartridge.This won't work.
Now then,let's try something different,shall we?
Ok you can try to extract your save file with Nintendo DS.I can't post links,but google this: " [HOW-TO] Back Up and Restore Retail GBA Save Games [Pokemon] " and click on the first video.
You will need a few things,check them in the video's description.
Now that you have your savefile,use one of the many methods to acquire Mew.You can use cheat codes,but Mew won't obey you.
Here's the best thing you can do:
Do this on VBA!!!
-Complete Emerald and use cheat codes to warp to Faraway Island or you can use a cheat for the ticket,but it's complicated to use the ticket (the game won't allow you to use it directly ).
-Now just trade Mew to Fire Red.