No, you can't.
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It is impossible to obtain a Mew in Pokemon Emerald outside of Nintendo events without cheating or trading from another game.
you don't. You can't find either Mew or Mewtwo in Emerald; you have to trade from FireRed or LeafGreen to get Mewtwo. You can't get Mew without an event or cheating.
You can't catch Mew with cheating except in Pokémon Eemerald but that's with a special event which is no longer possible however you can catch Mew in Pokemon Diamond and Pearl via cheating device on Action Replay however there is not official way to catch Mew without cheating except in the first generation (only in Red and Blue) you could do a series of walking places and pressing buttons which was a glitch in the game's programming.
where to find a azure flute without action replay and cheating in pokemon platinum