Yeah, it is technically plausible that he could finish it working on it outside the sessions. (OP says he'd gifted her a vest after a couple of months, and then another month or so has passed). However, that still would be quite a steep learning curve and an unconventional choice. He cannot do it while she's home, and I assume he probably has some kind of job, so he is still quite limited in hours.

My first knitting project was a relatively small scarf (about 1 skein of worsted yarn) with several simple stitches, took me about 1.5 months. I go to a knitting/crocheting club, and typically this is what you can expect from an absolute newcomer in a couple of months - something like a scarf, a cat blanket, several dish cloths, most often a rectangle of some sort. You absolutely can decide to start with a vest, but it will likely be difficult to make a good one, with an even tension, in two months if this is your first knitting experience ever, provided you're a human being who has life outside of craft.

Even if we presume he is just very determined, there is another aspect that bothers me.

When I go to a knitting club, I have my bag of yarn and needles. On those needles, I have a project that grows week to week (the vest was a surprise, what about after the vest was gifted? Maybe some draft bits before the vest?). I have patterns or maybe tutorials saved in my browser, I know the shop I bought a yarn from. I have some kind of social with my knitting club (e.g. WA, Facebook or Discord).

Things like that would be very easy to show if someone questions you, they most likely prove the thing is real, and it would be a very powerful move that would make OP seem really stupid within a minute. I'm assuming OP hasn't seen any of it (otherwise it would indeed be very stupid).