Commonly available in Latin America

www.pagoefectivo.la

You select 'pay in cash' in the online checkout, walk to your neighborhood convenience mart, and they scan a QR code (or you give them a code if you don't have a smartphone) linked to your checkout session. It rings up the total, and you pay the clerk in cash. Once you hand over the cash and the clerk hits confirm in their POS system, the online store is notified instantly that you have paid, and your order moves directly into processing or shipping.

In Israel, we used to have post-office issued debit cards. You buy the card at the counter, with cash, and then it could be used for online payments, until you exhaust your credit. This is not entirely different from a bank, of course, but it allowed users to separate their purchases history from their income history.

Post office is also used for things like utility payments. You can pay them online, or write down the invoice id, the recipient, and pay with cash at the post office. I'm not sure how it works from the recipient perspective: i.e. how would you register your business with the post office, but, the existence of some such payments implies it should be possible.

NB. Also, technically, these services while physically provided in the post office are sometimes referred to as being provide by "postal bank". I'm not sure why it's called a bank though, since it doesn't provide key banking services s.a. loans or check-in accounts... Maybe it's just a "historic" name.