Mew must be traded from Pokemon Emerald after obtaining the Old Sea Chart and travelling to Faraway Island. None of the other Pokemon versions which are able to trade to FireRed have Mew as a possible Pokemon to capture. Of course, there are a number of hacking devices which can make Mew available in FireRed, but as in-game wise, there is only the option of tradin
So yeah it is Event only on Pokemon Emerald, then you have to trade. No catching whatsoever.