In the original 60s run, the implication is mutation is caused by nuclear radiation. In #1 Xavier says he believes he is the first mutant, and his parents worked on the A-Bomb. The idea of an “X-Gene” or “X-Factor” comes much later and isn’t why they’re called X-Men. (1/?) https://twitter.com/cockroacharles/status/1304986620232232960

Later in that run, Lorna Dane’s latent power is activated artificially. In the 1975 relaunch, the living island Krakoa is identified as a mutant by Cerebro, and again the implication is that this is due to radition, not a genetic factor (Krakoa is not remotely human). (2/?)

Unless I’m forgetting something, the first implications that mutancy is a genetic factor pop up with the character of Moira McTaggert, who won the Nobel Prize for her work in genetics. This is from #127, where she’s discussing her dangerous mutant son, Proteus. (3/?)

I can’t recall when the term “x-gene” is first used, but in the 80s:90s there’s a ton of back-and-forth between Moira, Beast, and Mr. Sinister arguing over how it works. The intro of ancient mutants like Selene and Apocalypse makes it clear nuclear radiation isn’t the root cause.

IIRC in the 90s Moira manages to map the mutant genome when she’s studying the Legacy Virus? But whether it’s one gene or a combination of factors has never been consistently explained. Basically it depends on the writer.

(The retcon explanation is that mutants are yet another Celestial experiment left to grow wild, like the Eternals and Deviants. But that doesn’t explain how it works.)

Basically: under Lee and Kirby, it wasn’t genetic, it was a side effect of nuclear power. When Claremont turned the X-Men into an explicit metaphor for oppressed minorities, he began implying much more strongly that it was a genetic heritable thing.

And then he created mutant characters like Selene who were born thousands of years before nuclear power, essentially negating the earlier explanation.

There’s no good explanation for Krakoa registering on Cerebro as a mutant in Giant-Size #1. The Marvel Universe Appendix (a really wonderful fan site) suggests that Krakoa tricked Cerebro somehow in order to lure mutants to feed on: http://www.marvunapp.com/Appendix2/krakoaxmen.htm

Given that in the 60s Cerebro also detected Juggernaut (never a mutant) and Quicksilver and the Scarlet Witch (no longer mutants, thanks to a goofy retcon), it’s possible the early version just wasn’t very precise. That would make sense if Xavier didn’t know yet it was genetic.

In 1980, in a What If? issue of all things. https://twitter.com/thecookieriot/status/1305017171567808512

In more recent stuff Beast has claimed it’s carried on the 23rd chromosome, and Storm once said she believes it’s a sex-linked trait passed through the mother — but that doesn’t really explain cases like Polaris (a weird anomaly all around) or all of Sinister’s mutant eugenics.

Basically: we will never know because it’s constantly contradicted in-universe, which is probably for the best. I can’t remember the first time someone says the phrase “x-gene”, so I’m sorry I didn’t answer your actual question lol

Oh and the original 60s framing that mutants were caused by nuclear radiation and nuclear weapons testing is why the X-Men are called “the Children of the Atom”, but I’m sure there’s a biochem way to make that nickname still make sense. (I was a humanities guy; don’t ask me.)