No. Just no. The Webb telescope will never be able to capture light emitting from the Earth 2,000 years ago, because to be able to do that the telescope would have to be 2,000 light years from the Earth. While that distance is minuscule on cosmic scales, it would still take 2,000 years at the speed of light to get the telescope to that point in space. It would then take another 2,000 years to get the data back to Earth.

It would take much, much longer than that (even using advanced technologies that we don't yet possess) to propel the telescope to that point at even a significant fraction of the speed of light.

Traveling beyond the speed of light is not possible, despite your inaccurate reference to physicists speculating about something very different.