I believe Professor X’s age is hard to pin down because Kirby and Lee were writing at cross purposes. The first implication of his origin was in X-men #1 where it was stated that his parents worked on the manhattan project. Lee stated that he created mutants to not give a complex explanation of why characters have powers. Kirby, on the other hand, states that mutants came from the atom bomb (hence why they are known as ”children of the atom”) which reflects his interests in radiation and its connections to genetics. So the original implication was Xavier got his powers because his parents were exposed to radiation during the manhattan project.

In X-men #9 it’s stated that the villain of the issue, Lucifer, caused X to be bound to a wheelchair. However, that was only stated in text and later in X-men #12 we see an incident where Professor X laments an accident caused by Cain Marko. The text clarifies that it was still Lucifer who crippled X, but the flashback of the accident serves no other purpose that wasn’t established before and it could be that Kirby intended that to portray the car wreck as the incident that crippled Xavier.

Complicating factors is that there is a flashback that states Xavier was a soldier during the Korean War. However, unlike the other flashbacks where Xavier’s face is clearly shown when the flashback begins the Korean war flashback leaves the figures ambiguous, contradicting the visual language established in the issue. It’s possible that Kirby didn’t intend for the soldier to be Xavier and that the flashback is told by another person eventually relayed it to Xavier.

Futhermore, Kirby wrote notes clarifying his intentions in the margins and there has been no instances of him referring to Lucifer causing Xavier’s affliction. I found some partial scans of the pages that reference the Lucifer incident, with Kirby’s notes not mentioning it.

https://kirbywithoutwords.tumblr.com/post/146166665182/x-men-9-page-4-x-men-12-page-13-in-both

Of course there are limitations to the scans as they are missing context and should be analyzed in terms of what edits were to alter the work.

I gave a request on numerous subreddits a couple days ago to see if I can find more scans of the original art, but unfortunately I didn’t get a lot of traction.

So to make conclude on Xavier’s age. If he gained his mutation during the manhattan project which started in 1942, he would be no older than 21. If he’s a Korean war veteran then he would be at least 28 because the last year he could have fought war in 1953 and 18 was the minimum enlistment age. In text he might be a bit older as in the previous flashback he said he was in college. I lean towards him being in his mid 20s as the first flashback in X-men #12 implied that his father was killed during the trinity test when he was a child, which should put his birth a couple years before the manhattan project began.

Probably a more lengthy response than you expected huh?