Hello Raclette, 2.5 years, that's a bit early. The Schwimmverein beider Basel has some
courses for 2-4 years olds which require the presence of a parent. They emphasize that it's more of a gymnastics course than real swimming lessons. These begin at 4.5 years.
Just in case you didn't know, swimming lessons are part of the education in the elementary school.
(Another sidenote, Swiss bademeister have less responsability than US pool attendants, that is to say that not the entire pool/lake is under surveillance all the time. It is expected that parents keep an eye on their kids.)
I have no experience with the Schwimmverein beider Basel, just found the website on the internet.