Ways faster-than-light travel could be fun, while also trying to solve Fermi Paradox.
1. It’s actually hard to go slow.
I’m going to call this a Tachyon Drive approach. Once you spin up a tachyon drive, you actually go infinitely fast, and it takes precision and energy to slow the heck down. Most of the first ships are lost because they just go beyond the bounds of the visible universe. Even when you eventually want to make a jaunt over to Alpha Centauri, a tachyon drive jump lasting a few seconds, followed by a year-long slow boat inter-system, is considered normal and expected.
2. Better Space
In the hyperdrive model of FTL travel, the drive system temporarily puts the ship elsewhere – into a type of space different than our universe. So, we put all this effort into making this drive system, and the first time someone spins it up, turns out that hyperspace is just…better in like every way. Most hyperspace is fiction is unlivable, harsh, or full of evil beings. But in this version, it’s just better: stars and planetary systems are way less farther apart, space has atmosphere so you can breath in it (it’s just kind of chilly), there’s frequent entropy reduction events. Every non-luddite of every civilization emigrates from our universe to that universe as quickly as possible.
3. Wormhole Dispersion
An Einstein-Rosen Bridge, as a singularity, allows space to be irrelevant, so by passing through it, you can exit through any other Einstein-Rosen Bridges in the universe. Well, turns out that passing through all the other ones is mandatory, so when you enter, you are split into infinitesimal pieces, and exit as radiation from the event horizon of every other black hole in the universe. Normally you’d think this formal of travel would be useless, and you’re right, but if you quantumly-entangle the entire ship to…itself…somehow…before entering, your vessel, and your body, can still technically be attached to the other parts of itself. So, it’s more of an ascendance to an ethereal plane than travel to be honest. If you don’t do the quantum entangling step before entering the black hole you die though.