It's been tackled a few ways. The Star Trek Legacy game goes with the... very difficult to reconcile idea of the Borg as the result of one vulcan scientist from Archer's era having weird ideas. There's also the 'Shatnerverse' which had its own take, mentioned by tidewatersouthern. The main novelverse tackled the idea as part of the 'Destiny' trilogy, with a rather elaborate backstory, revealing them to be a time displaced offshoot of a species called the Caeliar; Captain Hernandez discovered them, the whole species accidentally gets flung back in time, with an asshole named Sedin in particular finding herself so desperate to survive, that she forcefully assimilated the others, resulting in the first Borg. Which are named such because one of the humans absorbed in the process was thinking how they didn't want to be turned into cyborg
Just as Discovery season 2 is partly a way of making use of the concept of Control while thoroughly nixing the way it was depicted in the novels from being considered in any way part of canon, Star Trek Picard's general use of the Borg seems partly geared to make sure the Star Trek Destiny novels - which had a large Borg invasion as the big threat - weren't possible anymore
Interesting, I could see a survival aspect of it being cool but not a tech from the future kinda thing, the Borg are powerful because of how many cultures they've assimilated, I feel that makes them scarier (well before they got killed off)