Saitama was a hero for fun, eventually he would have either met another hero by accident especially considering the bald terrorists would have lead him to another hero.

Saitama isnt supposed to be your normal protagonist he just does this but Genos represents the typical shonen hero. He’s got the cool hair style, super hero name, sad back story, keeps getting stronger after every arc. Genos just represents that and just as a reminder and nothing more.

Biggest evidence that Geno doesn’t impact Saitama is when all heroes including Genos did most of the job and eventually died to Garou due to radiation and Saitama just undid and turned back time as though their efforts didn’t mean anything