How can you get a mew in Pokemon fire red without cheats?

There's a high probability that there's no way to get Mew in Pokémon FireRed without using a cheat device. If there were any way other than to use a glitch to obtain Mew, people would've figured it out ages ago.

I'm sorry man. I know how you feel. I really want to catch Mew as well... :(

It's impossible. The only way to obtain it legitimately was to go to an event where it was being distributed, all of which have long long since ended.