"Chronological evidence that the Moon is either young or did not have a global magma ocean."

The impact likely happened very early in the Lunar history: at the time when magma ocean still existed or just ceased to exist.

Immediately after the impact, the Earth's mantle was vigorously convecting, the surface was a large magma ocean.

If anything lived in the magma oceans, it was beyond their powers to identify.

It is also possible that terrestrial planets had magma oceans at some point during their formation as a result of giant impacts.

A magma ocean is thought to be present on Io.

The whole surface of the planet becomes one single magma ocean, and all the heat of the interior is released at once.

This structure is thought to have developed through the fractional crystallization of a global magma ocean shortly after the Moon's formation 4.5 billion years ago.

In other words, the magma oceans cooled fairly quickly.

As the Moon formed, the outer part of it is thought to have been molten, a "lunar magma ocean."