Is it a good idea to create an index just for new data to increase index creation performance?
if you create a partial index then your queries will have also include the condition used to create the index. if they do not the index will be of no use.

when creating the index there will probably need to be a scan of the entire table your only win is a smaller index size.

What index will help queries most depends on what information you want from the table. are you sure that there are enough payments with the exact same creation that including userid as the second term in the index is justified? bear in mind that timestamp is 8 bytes while numeric(20) is 16 bytes, so an index on timestamp only will also be more compact.

An index on payment (userid, creation) will be more useful in the case where you want you find the most recent record, or the payment history, for any particular userid.