How to connect wires coming from bottom side of a single-layer PCB?
There is a product from Molex that might be designed specifically four your use case.
It is called: Bottom-Entry Lite-Trap SMT Wire-to-Board Connector
And it looks like that:

There will still be machining to do on the PCB, in order to allow the connector housing through, but the result will be solder-free and super clean looking, I think.
But for 20 connections it will set you back 14$ per PCB just in connectors, wether it is worth it or not I will let you be the judge of that.
https://www.japanese.molex.com/molex/products/part-detail/pcb_receptacles/1042660110
https://www.digikey.com/product-detail/en/molex/1042660110/WM12961CT-ND/5980647