Ash starts his journey at 10. This is a fact, I don't need evidence for that. So- Indigo League starts, Ash is 10. In the episode of Season 2, "The Battle of the Badge", Ash states it's been 1 year since they started out, as the screenshot shows. He's 11 now, as of Indigo season 2. Then Team Rocket comes into play. For the sake of things let's say Jessie is 25 when the show starts. She'd be 26 by season 2. In an XY episode, forgot the title but it's the Gourgeist Festival one, Jessie mentions her Pumpkaboo remembered her birthday when James and Meowth didn't. Her having a birthday means she's a year older, so now she'd be 27. MEANING that Ash is now 12, because a year has passed. Jessie's birthday is before his, meaning he'd be VERY close to 12 if not already 12. Seeing as episode 1 takes place on his BIRTHDAY and Jessie's already her starting age, ~25, then Ash would be closing in on 12. More than likely by Sun and Moon or Journeys, Ash's birthday has happened, making him at the series' end: 12 years old. ALL of this is backed by canon, you just have to think hard on it. Now the answer of "Why doesn't Ash age at all" has been found: He does age, he just does it slowly and doesn't show as much. But time DOES in fact pass as he travels. Something else worth noting is in XY during the Gourgeist Festival, seeing as it's their version of Halloween, would be expected to be in around October. And Sun and Moon has Ash in school, so assuming he started at the BEGINNING of the school year, that means he spent an entire year in Kalos after the festival before going to school in Sun and Moon, making him ~13 when his journey ends. However, there's no canon confirmation that the festival was actually in October, so honestly, we can only rely on canon confirmed ages rather than speculative dates. It's possible he's even older than 12 but for now we can stick with 12.
Space/click to change the screenshot. Evidence are screenshots taken directly from the episodes (available on YT btw! you can investigate yourself if you want) Disclaimer: I have only Indigo League, Orange Islands, Johto Journeys, XY, and parts of Sun and Moon. I gathered all this from the anime bits I HAVE seen, there may be more info out there I just haven't seen yet. I dunno if there's another yearly skip between Idigo League season 2 and XY because I haven't seen an episode proving there is, making Ash 13 when his journey ends. But I'm watching through the entire anime so if I see even more evidence, like something that will tell us how old Jessie, James, or another character is, I'll let yall know if yall want.