So there is a way to get Mew without an event (at least in the original Game Boy copies), however there are certain conditions in order to get it.
1. The trainer on the grass near the Nugget Bridge on Route 24 must not be fought.
2. The trainer on Route 25 with a Level 17 Slowpoke must not be fought.
Now to get Mew as early as possible:
1. Catch an Abra (preferably at Route 5) and add it to your party. (Make sure your last Pokemon Center visited was Cerulean City's, and you have plenty of Poke Balls)
2. Go to Route 24, go up to the top of the river and walk left until you can walk down. Make sure to hold down and Start at approximately the same time to move down and immediately pause the game while in the Trainer's line of sight. Use Abra's Teleport to warp to Cerulean City (the trainer should notice you before you teleport), go up to Route 25, and hug the upper wall when battling the Slowpoke trainer so he walks up to you.
3. Defeat the trainer, then walk left back to Route 24 without battling any other trainers then the pause menu should pop up automatically. Exit out of the pause menu and a battle with a Level 7 Mew should occur. (You can lower the level by using Growl on the Slowpoke a total of 6 times to reduce the level of the Mew, however if Growl is used 6 times the Mew would be Level 1, then the Mew would auto-level to Level 100 while only knowing Pound.)
I hope this trick is kept in the VC release, I'd like to have a Mew on my team.
1. The trainer on the grass near the Nugget Bridge on Route 24 must not be fought.
2. The trainer on Route 25 with a Level 17 Slowpoke must not be fought.
Now to get Mew as early as possible:
1. Catch an Abra (preferably at Route 5) and add it to your party. (Make sure your last Pokemon Center visited was Cerulean City's, and you have plenty of Poke Balls)
2. Go to Route 24, go up to the top of the river and walk left until you can walk down. Make sure to hold down and Start at approximately the same time to move down and immediately pause the game while in the Trainer's line of sight. Use Abra's Teleport to warp to Cerulean City (the trainer should notice you before you teleport), go up to Route 25, and hug the upper wall when battling the Slowpoke trainer so he walks up to you.
3. Defeat the trainer, then walk left back to Route 24 without battling any other trainers then the pause menu should pop up automatically. Exit out of the pause menu and a battle with a Level 7 Mew should occur. (You can lower the level by using Growl on the Slowpoke a total of 6 times to reduce the level of the Mew, however if Growl is used 6 times the Mew would be Level 1, then the Mew would auto-level to Level 100 while only knowing Pound.)
I hope this trick is kept in the VC release, I'd like to have a Mew on my team.