Geologist here -- this has been an active topic lately!
Just a few weeks ago there was a paper proposing a 4.336 +/- 0.031 Ga age for the Lunar Magma Ocean [1], which is often equated with (esp. in public press [e.g., 2], though not really the same as) the age of the Moon. For comparison, the "40 to 60 Ma after solar system formation" in the new paper [3] discussed here translates into roughly 4.517 +/- 0.010 Ga.
This new paper agrees almost perfectly with one I was a coauthor on a couple years ago though [4], which also gave an age of 4.51 (+/- 0.01) Ga, so maybe we're starting to get slightly closer to some consensus.
[1] https://doi.org/10.1016/j.epsl.2019.07.008
[2] https://www.newscientist.com/article/mg21128265-100-moon-may...