FTL starships in an SF story don’t need a detailed explanation, just a new invention.
It’s the exact same thing as a speculative story in the 1920s discussing supersonic flight, even though the jet engine hadn’t been invented yet.
For instance “Tunnel in the Sky” bypassed the whole issue in the 50’s, later imitated by “Stargate”…
True but at that point objects travelling faster than sound had been demonstrated.
It was just hard to engineer a manned plane that could do it. For example during WWII the V2 rockets travelled much faster than sound. They were just unmanned. Or more simple, bullets were supersonic for longer too.
What I mean is, nobody thought the sound barrier was a hard limit we could never break.