Leaving out that comma is not a grammar mistake. The comma slightly changes the feel of the sentence, but it's not wrong to include or omit it. But yeah, I agree with the other commenter that AI would be less likely than a human to omit the comma.
Adverbial clauses at the front of a sentence don't always have to have a comma. It's often taught this way to new English language learners or in style guides that want to keep things as unambiguous as possible because including the comma in that case is never wrong. But it's also sometimes optional.
One of the answers cites section 6.34 of the Chicago Manual of Style as follows: "Although an introductory adverbial phrase can usually be followed by a comma, it need not be unless misreading is likely. Shorter adverbial phrases are less likely to merit a comma than longer ones."
For the example we're discussing, "Back in 2022 or 2023", my personal instinct as a university-educated native US English speaker would be to include or omit the comma primarily depending on how much emphasis I want to put on the timing of my statement. I also know that I tend to write overly long sentences with too many commas, so sometimes I'd intentionally counteract my own tendency and limit the complexity of the sentence by removing a comma like that if the sentence still seems good without it. Other times I'd split the sentence into two, but my sentences rarely get as staccato as AI-written ones.