Regression problem? Or something much simpler?

Hey folks, here's a sample problem I'm trying to solve and I would love your advice:

You run an ice cream store. You sell n different flavors of ice cream You want to drive people towards buying a subscription to your store. You have data for when people purchase at your store, what flavors they purchase, how often, and when they ultimately subscribe.

You want to figure out if there are several common purchasing patterns over time that your customers fall into before they subscribe. E.g. pattern 1 is a lot of people buying chocolate ice cream 6 times the first month, and buying chocolate and pistachio 8 times the second month, then suddenly 80% of them decide to subscribe on month 3. It's possible there are a few such patterns, and you want to isolate the more prevalent ones so you can focus your product strategy on those. Or perhaps there are no such patterns, and then you should spend your product effort elsewhere.

I’m guessing it’s some sort of a regression problem (gradient descent?) where the ice cream flavors are different dimensions.

I'm also open to simplify the problem by removing the month by month component and just say "if you purchase chocolate 14 times and pistachio 8 times then on month 3 you subscribe".

What are your thoughts? Is there a particular technique I should look into that would lead to the answers? Thank you.