The answer X gave was beautiful, but I also know another way if the Pokeball plus isn't an option.
All the glitches in the original Red and Blue games are still available within the Virtual Console releases, and this includes the Mew Glitch. The Mew Glitch is a glitch in the game you can do early on to trigger a legit encounter with Mew.
Using Bank and Home, you could bring the Mew up to the newest games. Since a glitch isn't hacking, it's still considered a legit Mew
Here is a guide if you're interested in learning: https://youtu.be/yXbl-hNxnS8