PostgreSQL 11 was released 2018-10-18 and became available in RDS generally 2019-03-13.
So about 6 months.
AWS does have a preview available, so you can try it for non production workloads and report problems if any. That should speed up the GA release as well.
That was mostly because they held off releasing it until some bugs were resolved. Otherwise it probably would have come sooner.
PostreSQL 10 was 2017-10-05 to 2018-02-27.
10 took 146 days, 11 took 145 days. Just a tad under 5 months for both.
Historically 5 to 6 months, unfortunately.
I think google cloud sql JUST got postgres 11, so it is even longer over in GCE land ;(
But far better than Google Cloud SQL, which never got PG 10 and only just got PG 11…last week.