It might be in The Bookseller, which often lists new acquisitions, especially if there’s an auction involving several publishers or a big advance — though there’s no particular reason to think TSP had either. But I don’t subscribe to it TB, so can’t search.
There’s quite a long lead-in in fiction, which I know better. If TSP came out in 2018 around the time Tim was doing his finals, yes, perfectly possible the advance was paid a year or more earlier?
She does mention (again around Tim getting his BSc) that they’re living on ‘the tail end of a student loan and an advance on the book’ and when they’re taking on the cider farm but still living in Polruan because the house is uninhabitable, and they have to pay two debts for a couple of months, she says ‘the advance on the book couldn’t last forever and there was no way of knowing if the sakes would increase or if it would disappear into obscurity.’ (It’s not out in paperback yet at this point.)
I have literally no idea what type of advance she’d have had, though.