Does the Big Bang Theory explain how the earth was formed?

No

theory explains how the universe came into existence.

There are several theories as to how formed. My favourite one is that every planet started off as a gas giant, but the terrestrial planets lost the atmosphere due to the solar wind.

The big bang theory cannot explain how Earth was created, and vice versa. If the theory of how the Earth was created is proven wrong, it would not disprove the big bang theory. If the big bang theory is proven wrong, it would not disprove the theory of how the Earth formed.