Fighting the Youngster will always result in a Mew encounter because his Slowpoke has a Special of 21 (15 in hex). But if you fight something else before returning to Route 8, it will change which Pokémon you encounter. If you don't know how to catch Mew in Pokemon Red Blue or Yellow see it here on gamezplay.
Let's say you foolishly choose a starting Pokémon other than Bulbasaur and want to make up for it. Bulbasaur's hex number is 99, which converts to 153 in decimal. Now, you could fight a wild Pokémon with a Special of 153, but the only place to find that is on a Level 64 Chansey in the Unknown Dungeon, and those Chansey are quite rare. Worse, they only have a one-in-sixteen chance of having the right Special. Fortunately, there is a solution: Ditto's Transform, which copies the stats of the opponent.