May's Wartortle was received from Professor Oak while it was a Squirtle.
It debuted in The Right Place at the Right Mime. Squirtle became attached to May while she was visiting Professor Oak's lab and decided to travel with her. It instantly took a liking to contests and learned Ice Beam without any training in order to defeat Team Rocket. Seeing Squirtle's potential in contests and in battle, May used it many times in Kanto, including her battle with Drew in the Kanto Grand Festival where Squirtle defeated Flygon before being defeated by Absol.
At some point before the Wallace Cup, squirtle evolved into Wartortle and learned Aqua Tail.