The Guest Data export found under Analytics > Data Export > Guest Data includes a "Guest Signup Date" field. This field indicates when a guest signed up for the loyalty program. There is another field in this export, Created At, that is tied to both loyalty and eClub users.
Users that are only eClub will not have a "Guest Signup Date" in the Guest Data export. These guests will show a "Created At" date. If an eClub user signs up for loyalty, then a "Guest Signup Date" will populate for the day that loyalty was joined, while the "Created At" date still reflects the day the guest was uploaded to eClub.
Loyalty users will have both a "Guest Signup Date" and a "Created At" date for the same day that the loyalty account was created.