Is there a way to define the "date/time first {event} done" for a user, similar to Date First Seen?

Context:

We’re trying to track initial purchases of users but are running into an issue where using “unique users” count by day of users who fired our “purchase” event: it is over-counting since a user can purchase on both Day 1 and then on Day 2 and still be unique within each day. 

My thought was to define a user property that is similar to the default property of “Date First Seen” that is the date or time of first “purchase” event. Is there a way to do this or otherwise back in to initial purchase dates without redefining what properties our event fires with on the backend?