Very little from the 30s (actually, nothing from Armstrong, though I suspect he was active then since he was born in 1901). Maybe just a limit of the technology available at the time, so not much was recorded in a recoverable way. Perhaps a phonograph was a luxury item, and people got it all from the radio. Not sure.

I don't think the problem was lack of recording. The record industry really started to launch in the early 1920's, with sales getting over 100 million units per year towards the end of the decade. Records themselves started off as more like advertisements for the sheet music, with most of the money coming in from the latter than the former (which reads like music videos in the early days of MTV). The Great Depression, more than radio, really did a number on sales.

Those original recordings aren't unrecoverable - they're obviously lower quality than a modern recording, but still listenable. One of the earliest breakout recorded pieces of the early era was apparently Swanee as sung by Al Jolson in 1920 (and one of Gershwin's biggest hits), which is here:

YouTube: Al Jolson - Swanee (1920) (CatsPjamas1)

...or legendarily talented Bessie Smith's Downhearted Blues from 1923:

YouTube: Bessie Smith - Down Hearted Blues [1923] (Classic Mood Experience)

Which, again, I'd be shocked if too many Gen Z'ers are out there "discovering" Al Jolson's or Bessie Smith's material, even though he was one of the biggest stars of the early days of recorded music and she was one of the most talented singers of her era. It's just too far back, I think, to be relevant to a modern audience - even though the songs themselves - the compositions rather than the performances - might still work.