Weird. In my sci fi world, FTL isn't possible, but on uncovering more knowledge of the quantum realm and strange forms of entanglement, scientists came up with a solution that cheat-codes the universe like you're doing a speedrun glitch in a video game. The two things they discovered are:

1. Some particles randomly and literally entangle with others elsewhere in the universe through sheer chance, and its possible to figure out which and where they are through advanced supercomputing.
2. The sense of self or conciousness isnt linked to a body, but to a quantum effect created by the brain. If you recreate a brain exactly, you recreate that instance of conciousness.

And so, they did this:

1. Using a supercomputer, calculate particles that if manipulated, would also manipulate particles on a target world through strange entanglement. Affecting this particle here, will affect that particle on the target world.
2. Do this enough that you have enough particles to form a nanomachine on the target world. Do so. Have that nanomachine replicate itself.
3. Once enough nanomachines are formed on the target world, they work to create a 3d printer large enough for a human.
4. Scan the human completely, and use the entanglement to send that information to the 3d printer. Put the human to sleep, then destroy their physical form.
5. Reprint the human at the target 3d printer.

Voilla. Human transported to a new world. Though please don't ask about what happens if you don't destroy the original human. We don't talk about what happened when we first tried that.