Magnetic striping on the sea floor [https://en.wikipedia.org/wiki/Plate_tectonics#Magnetic_strip...] is probably our best clue. It's the piece of evidence that sealed plate tectonic's place as the dominant theory.

Plates which are separating let molten rock from the mantle up, where it cools hardens. Any rock which can be magnetised (iron) is aligned with the Earth's magnetic field when molten, and gets fixed that way. The magnetic field swaps every 10,000 years or so [https://en.wikipedia.org/wiki/Geomagnetic_reversal], so you get a stripey effect.

Working our more precised dates for the magnetic swaps is a matter of slow and painstaking correlation with other bits of evidence: dating of radioactive elements, tree rings, rock layers, the temperature of the Earth, composition of gas bubbles trapped in rock and ice.

Paleomagnetism measurement of the magnetic field direction in a rock gives the latitude of a the rock when it formed. The magnetic fields are horizontal at the equator and vertical at the poles, thereby giving latitude of the rock when is cooled from volcanic hardening or the last metamorphic squeeze. And there is a magnetic imprint when sediments settle too.

Latitude when combined with geometric constraints of seafloor strips and correlated trans-ocean rock formations build the overall picture.

In addition the oldest seafloor is 220 million years old or 5% of Earths lifetime. Paleomag measurements go back ten times longer.

Those are fun and interesting corrections, thank you.

And palaeontology.

There may be tens of thousand of research papers behind each map shown in the OP. It is like solving a puzzle. At location X, Scientist A finds some clues in plate tectonics, Scientist B finds something in geochemistry, and Scientist C finds something in fossil records. Then they piece them together and if these stories all tell the same thing without a serious conflict, you can construct a point on that map. Now imagine doing this for thousands of different regions involving several generations of scientists, you get nice maps like these.

This Wikipedia page would be a nice read: https://en.wikipedia.org/wiki/History_of_Earth.

Plate tectonics and Continental drift ??

And geochemistry.

The geochemistry goes without saying.