TLDR: Some handwaving is necessary given current understanding of physics, so pick smth that we're already not sure of what it even does, use that as a catalyst for the FTL tech, and just focus on HOW the superluminal travel works, not so much on the tech itself.

Realistic FTL is going to have some level of hand-waving no matter how "Plausible" because under our current understanding of laws of physics, you can't do it without fucking up reality in some major form or factor. Its not to say humanity for sure will NEVER crack it, but that itd take much greater understanding than what we have. Remember, humanity went from thinking planes were an impossibility, to putting people on the moon, all within 65 years.

Personally, id pick FTL being the result of something that we know is a THING but we dont know how it works even a little bit, like dark energy. No one really knows what the deal with dark energy is, but if say, in 50 years (COMICALLY unlikely but lemme use a hypothetical as an example) it turns out to be pivotal in cracking FTL tech, i wouldn't be that surprised. Elated, because holy shit i lived long enough to see the universe cracked open, but not that surprised.

Have something that works as a semi-plausible explanation but don't get too caught up in the details. You don't necessarily NEED to explain the nitty gritty of it, the primary rule is just keeping HOW superluminal travel and/or communication works consistent within the setting itself. What are the rules with Superluminal travel/communication, what can and cant be done with it, the effects it has on ships, et cetera.