When is a new customer invited to add my loyalty card, and can I change the timing?

After their first order, once per customer, at a delay you choose. The Invitation tab on the loyalty card screen under Marketing has a box for how many hours after the first order it goes, from 1 to 168, with 4 as the default so it arrives after the food rather than while they wait. Anything due outside 10:00 to 21:00 waits for the morning. There is no on and off switch for it on purpose: it is part of offering the card, and it stops the day you switch the loyalty programme off. The Loyalty & rewards tab in the docs has a guide on the invitation.