If entanglement is a fact, and it seems to be, time travel is impossible.
Indeed, if all elementary particles, of which we are made 100%, are entangled with all the other elementary particles with which they ever been in contact, and if they were in contact with every bit of energy in the initial pre-Big Bang “singularity,” there is not enough energy in the whole universe to go even one microsecond in the past or the future since it is the whole universe that would be affected by “these time travels” because of this universal entanglement affecting all elementary particles of the universe.

To put it another way, at the level of elementary particle movement in the future are indeterminate, while their movement back in the past would have to be determinate to return at the same universal state at which they were at this moment in time. And Quantum mechanics precludes such a determinate movement in time, for good reason if entanglement is a fact.