Could humans actually travel through time?

Every GPS satellite is a working time machine. Their onboard clocks are deliberately offset because relativity shifts them by tens of microseconds per day relative to the ground.

Scale that effect up and forward time travel becomes a transport problem rather than a physics problem: accelerate close to light speed, return, and decades will have passed at home while months passed for you.

Backwards is different. Closed timelike curves appear in some solutions to Einstein's equations, but every known route requires negative energy density, and quantum effects may destroy the passage before anything crosses it.