Why do astrophysicists believe they could study the origins of the universe easier from the moon than they can on earth?
The Moon's lack of erosion, atmosphere, and magnetosphere all provide ways to better study the origins of the Universe.
There are at least a couple of reasons for this belief.
One is that there is very little erosion on the Moon. This matters because there are a lot of questions concerning the beginnings of the Solar System (and thus, by extension, the Universe) that can be studied through examination of asteroids and meteors (there have been recent space missions to examine and analyze core samples from meteors).
An easier way to examine meteors is to see the area where they have impacted and look at what is left of what crashed into the planet. And in the early formation of the Earth and Moon, meteors routinely smashed into them. Geologists do examine meteor remnants here on Earth but because of erosion and the effects of life on Earth, there isn't much to see and examine.
The same is not true on the Moon - the craters that we can see on the Moon are from that early age of creation. Much could be learned about the early beginnings of the Solar System if we were able to examine closely those impact craters.
Another reason for the Moon being an easier place to study from is its lack of atmosphere and magnetic field. Here on Earth, light and other electromagnetic waves have to pass through both a lot of air (the atmosphere) but also magnetic fields (the magnetosphere), each of which makes "seeing" (a word that refers to the ability to clearly see objects in space) difficult, if not impossible.
The Moon has no such constraints. Telescopes built on the Moon wouldn't have to contend with weather events, clouds, magnetic fields, and the like, which would make for better seeing. And telescopes could be built much bigger than telescopes such as the Hubble Space Telescope - there is no limitation as to what can be built based on a rocket's ability to carry it up to orbit.
And it's the ability to see clearly into the deepest recesses of space that provide our best look into the beginnings of the Universe. Looking deeper and deeper into space is the same as looking back through time (because light travels at the speed of light, the more distant we can look the longer the light has been travelling, and so the further into time we are looking).