Creating big indexes - Mailing list pgsql-general

We have a few tables having size ~5TB and are partitioned on a timestamp column. They have ~90 partitions in them and are storing 90 days of data. We want to create a couple of indexes on those tables. They are getting the incoming transactions(mainly inserts) 24/7 , which are mostly happening on the current day/live partition. Its RDS postgres version 15.4. So in this situation

Should we go with below i.e one time create index command on the table..

CREATE INDEX CONCURRENTLY idx1 ON tab(column_name);
Or
create index on individual partitions from different sessions, say for example create indexes on 30 partitions each from three different sessions so as to finish all the 90 partitions faster?
CREATE INDEX CONCURRENTLY idx1 ON tab_part1(column_name);
CREATE INDEX CONCURRENTLY idx1 ON tab_part2(column_name);

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Basically I have three questions:
1)If we can do this index creation activity online without impacting the incoming transactions or do we have to take down time for this activity?
2)If we can't do it online then , what is the fastest method to do this index creation activity ?