Short Answer: You could just build a model to predict purchase (0/1) and call it a day. Create a feature that is count of past purchases to control for repeat customers. BUT if you want to specifically deal with the time component (which is certainly more interesting)...
TTE Models: You should look at Time-to-Event models (accelerated time failure model, etc.) Normally, the event (0/1) is usually something phrased as a negative outcome (like death or loan default), but this is just because of the research fields these models stem from. There is no reason you can't re-pose your outcome to be a purchase event.
Watch Out For: Dealing with Censoring in the data. See Here
Get creative, I can't really comment on great detail here because you didn't give a feel for your exact dataset but you might try and work your dependent variable into something more concrete, for example, time between first view of customer and first purchase, or time between most resent 2 purchases.
Think about the purchase time distribution. Essentially, start to think of ways of parameterizing the purchase-time distribution given some conditionals (customer tenure, total purchases, etc.) As you expand on this vein of thought you'll come across methods that will help. For (a simple) example, using EM to estimate the parameters of various purchase time conditional distributions.
Hope this helps!