Can I create a coupon now that only starts working next week?

Yes. Go to Marketing → Coupons and click + New coupon (or Edit an existing one).

1. Fill in the Code, Type and value.
2. Set Valid from to the start date and, if you want, Valid until to the end date.
3. Make sure Active is ticked.
4. Click Save coupon.

Before the start date, shoppers who try it see "This coupon is not active yet". The Validity column on the coupon list shows the dates you set.