We can change the group your members start in if needed. What I would generally suggest however, is instead of doing it that way, do it this way
1 - Copy your members group
2 - Set up the promotion rules
3 - Rename the original group to Newly Registered
and just let the system promote your current members
If you want to move them quicker, you can also just bulk move everyone to the new group if needed, So step 4 and 5 would be
4- Search members in Newly registered (and other criteria if needed)
5 - Mass move to Members group