>>3769554During the early expansion of the universe planets formed from irradiated dust clouds. In a weightless environment, gravity will pull even the smallest particles that come close to each other together.
Mass attracts mass. So the earth started off as space dust swirling around until the core formed over billions of years but it happens with lots of celestial bodies that at the same time the larger core is forming a smaller one will be near by and they often exchange particles at their periphery while they formed. Even today, swirling spirals is the most common formation of celestial groupings.
It's less that the moon was made from the earth as much as they formed at the same time using the same source materials. Like twins. Most celestial bodies have moons of some form. It's very common.
The random chaos after the big bang was a mess.
Saturn has 146 moons. They just aren't as hefty as our girl.