You cannot obtain Mew in Pokémon Ranger: Guardian Signs through normal gameplay. The game (2010) is often confused with “PokePark Wii.” Mew was exclusively distributed via a limited-time Nintendo Wi-Fi Connection event in 2010.
Transfer Mew from other games via Pokémon HOME (from Pokémon GO, Let’s Go, Sword/Shield, Scarlet/Violet or older gens via Bank). Guardian Signs itself cannot receive transfers.
Summary: Legitimate Mew in this game is unobtainable today. Play for the story and other Pokémon.