You ask about studying the sun in particular. The sun can be tracked by sundial shadows, and north-south-east-west aligned objects or landscape features to notch the rising and setting sun over time.
You can observe the sun directly by using a pinhole to project it on a surface.

Fun detail: Camera comes from "Camera obscura" meaning dark room; the term was coined by Kepler in 1604 in Latin, but in his Book of Optics, written in Cairo between 1012 and 1021, Ibn al-Haytham used the term “Al-Bayt al-Muthlim", translated into English as "dark room."

The projection of images using pinholes was already known in Europe then, long before light-sensitive film was first combined with a small "camera" and a pinhole to capture images in the 19th century. Roger Bacon described its use for the safe observation of eclipses back in the 13th century, using a holed curtain.

While Newgrange in Ireland (dated to 3200 BCE) does not have a built-in pinhole-- it's rock... the roof-box in the mound has a gap in the rock which is oriented such as the sun only hits it and dramatically illuminates the room right at the Winter Solistice.

It's not hard to wonder if a holed hide could have been put over that or similar flaps to create a true camera obscura for solar observations.

Next question is, there any evidence this could have happened in Mesoamerica? They had the mounds, they had the caves, they certainly had cloth or skins and needles to use, so there is no technical obstacle to doing so.

On Native America (PBS show), first episode, I saw video of the Caverna de Pedra Pintada in Monte Alegre State Park, Northern Brazil, as guided with Anna Roosevelt and Chris Davis (Archaeologists working on the cave) and I was arrested by a painted symbol which Chris Davis called a turtle symbol. I stopped and replayed it again after he said it so I could check my first impression which was 1) it was familiar and 2) not remotely a turtle.
I said to my companion," look, that's no turtle, stylized or not, that looks like a hide on a square wood frame! Don't you agree?" (probably antelope-- something with a short tail and long neck, head cut off, neck side down... I live in the north and I see a LOT of hides.)

It also was drawn with a red dot exactly in the middle. If my assumption was correct, then I wondered what a painting of a hide on a frame could signify in a cave in Northern Brazil. Hanging up furs to cure? And why the dot in middle?

Other paintings and landmarks in that setting related to to solar observations.

I propose that archaeologists thus far have misinterpreted this particular sign as a symbolic and failed to see the literal drawing of a holed hide on a frame, used to create a camera obscura to observe the sun.

But there's no "proof" so far, just evidence that remains to be interpreted.

But I will say, on an objective basis, Meso-American astronomers easily all the potential tools Roger Bacon had to observe an eclipse safely-- darkened rooms, something fully obscure (hides or tightly knit cloth) that they could make holes in and use as covers, and many darkened rooms-- man-made caves, underground rooms, all exist and are found at Chaco, for example.