There's no way to prove either way, since the hacks people use involve changing box data to reassign Pokémon species and stats etc. and/or adding an item that's already pre-programmed into the game to the inventory, either with a cheat device like Action Replay or by dumping a modified save file from something like PKHeX onto the cartridge. It's just a case of changing variables rather than modifying the actual code of the game so even scanning it with the official legality confirmation tools they use at tournaments wouldn't flag it, which is a problem even to this day where it's an open secret that a lot of competitive players inject Pokémon rather than train them legitimately - but since they use builds that
could exist in game, they get away with it.
Realistically the cartridge is almost definitely hacked, but that's only a 99% chance, not 100%. For the Mew to be legit, someone would have had to go out of their way to go to a limited-time event between July and August 2005 to have the item transferred over
and held on to the copy of the game for nearly twenty years before deciding to sell it, which is unlikely but still possible. The part that makes it more damning is that the save file also has
a lot of other legendaries (
PreserveTube archive) on it - some of which are identical suggesting the player used the in-game cloning glitch; but also others (the multiple shinies) that seem absurdly unrealistic of a collection especially since this was pre-online trading.
The shiny Entei she pulled up is definitely fake since its profile said it was caught at Lv. 5, while Entei can't be legally be caught at that low of a level - though that doesn't prove the cartridge itself was hacked, an innocent explanation would be that the player had been fooled into trading for it by someone else. Again though, we're talking
absurdly low odds.