The asteroid that hit our Earth at Chicxulub is estimated to have been about 12 miles across, generating a crater 110 miles across. It vaporized the impacting object, but left unusual amounts of shocked minerals and droplets of molten glass for us to find. And it made a mess of the entire planet, not helping the dinosaurs very much.
Now, going from a 12 mile asteroid hitting the Earth to something roughly the size of Mars, you can imagine you are doing another entire leap in how catastrophic your impact is. Mars is 4200 miles across. The Earth is around 7900 miles across. This is no longer a small object hitting a large object, but two objects which are reasonably close to each other in size, so the energy involved is going to be immense.
Some rock vaporization & liquefying is definitely in order. And here’s where various theories begin to diverge. The Moon’s rock and Earth’s rock are chemically close enough to each other that they should have once mostly been in the same place (namely on the Earth). So when this impacting object, which has been dubbed Theia, slammed into the earth, it’s thought that the core of Theia sank down into the core of the proto-Earth to join the Earth’s existing core. But a good chunk of material would have been flung out into space, both from Theia or from the Earth. These pieces of blasted off rock would have gradually collected back together to form the Moon. This is generally considered the most promising running theory, but it can’t explain a few details, so it still needs a little tweaking.