Just for completeness, what would be the most normal/colloquial way to express:

"In the early '20s..."
"After the mid '60s..."
"By the late '80s..."

I'm pretty sure that one could say, for example, "К концу восьмидесятых" to mean "by the late '80s," but I want to double-check with native speakers.

P.S. Most English-speaking editors would recommend using an apostrophe before abbreviated calendar decades (consistent with the general practice of using an apostrophe to show that a letter or syllable has been dropped):

"During the '90s, when I was in my 20s..."