Although the first splinter officially begins in 2373, it's existence depends on events in Destiny which cover a much larger span. Oblivion's Gate suggested the First Contact Borg may have had a different origin to the Destiny Borg, so I think it's a valid suggestion that it goes much further back.
Sure, you can nitpick such details if you like -- heck, my own DTI: The Collectors goes back 64 million years -- but the very existence of Harm's Way demonstrates that the official conceit for now is that the TOS-era novelverse is still valid until the shows say otherwise. That conceit may not hold up to detailed examination, but the same goes for many narrative conceits. Best not to conjecture in advance of actual events.