How do astronomers study earth's history?
Earth's history is generally studied by geoscientists with input and advice from astronomers.
The evidence of Earth's earliest history (prior to about 4 billion years) is primarily meteorites that have landed on Earth from the solar system and in some cases, Mars. This gives geologists some idea of this early Earth's history. However, there are very few rocks older than 4 billion years as most have been destroyed by plate tectonic cycling of rock back into the mantel.
Astronomers do play a role in studying planetary formation in other star systems. One early conclusions from this work is that there many, many ways for a solar system and Earth-like planets to form aside from the way it was done in our solar system.