As an Apple developer for 42 years I tried all permutations I could think of and found there is no way around the walled garden:
Apple Invites requires a mandatory iCloud+ account (minimal 0.99 euro/dollar per month) and a non-anonymous Apple ID requirement with credit card or bank account. It probably has a perpetual lock-in of your invite groups and tracking of all participants as well but I couldn't test this properly without paying 12 Euros.