https://hackaday.com/2018/09/17/a-1-linux-capable-hand-solderable-processor/
A (barely) hand-solderable Linux-able ARM SoC. US$1 each if you buy a full reel from a questionable supplier, and the package is a 176-lead LQFP (!) with half-millimeter pitch (!!) -- but still only ~US$3 for qty/1 from reputable sources, and it is /technically/ hand-workable if you've got a temperature-controlled iron with the right tip and a particularly steady hand. I'm impressed.
The bad news, though, is that it's an Allwinner part with all of the usual baggage. The /worse/ news is that it's actually ~6yrs old and plods along at 1GHz. Somehow I just don't see it running Android 9.0 Pie without melting down spectacularly -- although, it might be adequate for running eg Linux Mint or something similarly lightweight...
I wonder how cheaply one could manufacture a complete all-in-one PC with one of these...? Back-of-the-envelope calcs makes me think one could compete with those ~US$100-150 Atom z8300/z8350 MiniPCs on eBay and Amazon and AliExpress (none of which have screens built in, mind you), but I've been wrong before, for sure...