2 times ships are shown traveling at FTL but are minute:
At the beginning of Prometheus and Alien Covenant, and indication of travel through the billiard balls moving when they reach the destination threshold at LV223.
Great cases of discussion about FTL travel have been brought up in these places:
FTL Travel in the Alien universe has only ever been hinted to and not explicitly explained because to go into the science of it is not part of what the Alien Universe is about. Alien sits within the realm of Medium Science Fiction as opposed to Hard Science fiction where technology and physics are grounded in science fact.
In Aliens Colonial Marines: USS Sephora Gravity Well is assumed that it generates the gravity aboard the spacecraft. It could also be a method of propulsion for the ship.
I asked Alan Dean Foster what he would have done in the Alien: Covenant Novelisation instead of the solar sail, since it wasn't scientifically sound. He answered that he couldn't do anything that would directly contradict the visuals in the film, so he probably would have resorted to some handwaving...talked briefly about collecting dark energy, or something along those lines. Hollywood is about visuals; not science.
Only Voyager 1 has crossed into intersellar space travelling at 65,000km/h, it will take 80,000 years to reach our nearest neighbour Alpha Centauri assuming it was heading towards that direction.
Mark G. Millis who is a NASA alum and founder of the Tau Zero Foundation has written extensively on the possibility of different "forms of propulsion where the fundamental properties of matter and spacetime are used to create propulsive forces anywhere in space without having to carry and expel a reaction mass."
Long distance space travel requires an engine that can generate thrust without fuel, scientists at NASA’s Eagleworks Laboratories created the EmDrive, the physics-defying contraption ostensibly produces thrust simply by bouncing microwaves around inside a closed, cone-shaped cavity, no fuel required. A German team of scientists replicating the technology for testing have reported that “The ‘thrust’ is not coming from the EmDrive, but from some electromagnetic interaction,” to prevent extra electromagnetic interference between the drive, power amplifier, and the rest of the electronics, they need to be shielded from each other. A box made of mu metal will effectively create a region with only a tiny, tiny fraction of the Earth’s magnetic field inside. Unfortunately, the researchers did not have sufficient mu metal to shield all the cables and electronics. Installing more mu metal is a planned upgrade for future testing.