Conveniently the subreddit maintains a reading list! Mesopotamia falls under the ancient near east: https://www.reddit.com/r/AskHistorians/wiki/books/middleeast#wiki_ancient_near_east/#wiki_ancient_near_east

I'm in a very similar situation as yourself. I can vouch for Amanda Podany's very short introduction as a good starting point. It's very short! 120 pages, so you'll go over subjects that leave you wanting to know more but that's ok since it's an intro! You get a broad overview and see how all the major time periods fit together, and learn terminology that comes up in other works. It gives you a good starting point to dive deeper.

The area of study for your particular interest is referred to, at least within history departments, as belonging to prehistory. Most undergraduate history programs rarely delve into that period, as it’s considered to be the domain of the anthropology dept., specifically archeology.

Often an undergraduate history program will have one introductory history course that will devote no more than a lecture towards covering all of prehistory. You may find the odd first year humanities course that delves a bit further into aspects of the late Bronze Age. However, I would suspect that the majority of the courses you’d likely be interested in will be found within the department of archeology.

As for distance learning, there are a very limited number of accredited schools offering a full online program in archeology leading to a degree. Problem is that most online programs tend to offer only a smattering of such courses. This is due to the fact that the study of archeology is not all that popular, and the majority of advanced courses are considered to be more hands-on. You may have better luck in finding courses similar to what interests you by looking at an online program in anthropology.