I don't know, I've had fin rot pop up overnight. That's what happened to Nino. I woke up and he was missing chunks out of his dorsal/caudal and it was definitely fin rot (black tips, got worse in the following days, had to treat at a very high conc. salt to cure it). I'm guessing it was an aggressive bacterial fin rot. As a result, I don't think timing is necessarily a diagnostic tool.
Yet he doesn't have a dark edge around the end of his fins .
If there is no black edge then it isn't fin rot. He is either a fin biter or got it caught on something. Do you have plastic plants in the tank? Or any decor? If so, remove them and replace them with live or silk plants.
Treat him with just clean water like iheartmybettas suggested. You can also add Stess Coat to help his fins grow back. If you don't keep his water really clean then
you might see a secondary infection that will lead to true fin rot, which would be bad.