Well, data just doesn’t really flow at the speed of light. It’s a really really complicated thing to discuss in terms of physical circuits because the true picture involves considering how the EM field evolves. Electrons in a circuit move at extremely slow speeds, ~millimeters per second.

The good news is you don’t need to send information particularly fast to send it through time. Generally in physics, we build time travel systems by creating extremely curved spacetime that contains paths to the past, theoretically you could send light through such a path to transmit information back in time. As someone already mentioned, you generally need negative mass to construct these.

If you have negative mass there are three options I’m aware of:

1. Wormholes, stabilised and moved in the right way can form a link to the past (but only as far back as the moment they were created, this is true of all time machines as far as I know)
2. Rotating torii of spacetime. Spinning spacetime is well known for creating weird time travel effects, a related option is an infinitely long rotating cylinder.
3. A rotating warp drive. This thing will explode in a high energy shower of particles and thus it’ll be nearly impossible to use, but a friend of mine recently found a way to get particles to travel back in time through it.

If you want to send information into the distant future, you could get really fancy and scatter some light off of a black hole or something.