Unfortunately, you can't move or remove the Past Due stamp; We suggest to use a better Payment Terms so it will not show Past Due on the invoices if it's not necessary.
One way to resolve this issue is to create a Payment Term Called C.O.D as an example.
And set the Due Date to 1; this way, the invoice is not due immediately..
Then to make it easier set the Default Customer Payment Terms as C.O.D
So when a customer created automatically will assign C.O.D Terms to them, You can always change the specific Customer Payment Terms in their profile.