A global index on created_time does not seem to be warranted on a table that is also partitioned on created_time, no matter what the size of the intervals would be.
First, you already would gain the benefits of partition pruning for any query that makes use of a query for created_time for a specific range.
Once you have limited the partitions queried, it would be optimal to work on the data that is local to those partitions. Generally it is optimal, to have queries that only have to select from individual partitions so that multiple 'tables' do not have to be joined for satisfying the query.
I would advise if there is a need for more granular access to created_time within any given range selected (minute, hour, day, month, year), that you create the index as a local index, available in each partition. If you needed to do continued aggregation or range queries within each individual partition that could be done.
This would also allow you to age out older partitions as necessary for data that can be archived, easily by exchanging partitions with empty tables or dropping partitions outright.