Warp travel was established as possible in the 90s. While using a really big rocket and accelerating past c still looks to be impossible, it’s possible to warp space such that your effective speed is many times faster than c without actually going faster than c.
The problem is the energy requirements. Previously, we were looking at the entire mass energy of Jupiter as a lower bound to get us to Alpha Centauri. We would have to utterly destroy Jupiter, getting rid of all its mass and gravitational influence on our solar system, to get to Alpha Centauri. Even if we had a way to do this, this would have consequences, and they probably wouldn’t be pretty- a lot of Earths habitability is due to where our orbit is, and that would change if Jupiter went away. Oh, then we’d need to destroy another Jupiter equivalent to get home.
With some tweaks to the original concept, the lower bound of energy requirements might be closer to a ton. One ton. This is probably smaller than your car.
There’s still a lot of work to be done before this is even at a proof of concept, but with the energy requirements reduced to this degree, it’s actually worth some research money to see if we can actually build this thing.