"At the beginning" or "in the beginning"?

They are valid but not interchangeable. I think the most important difference is that "in the beginning" seems to be an expression describing a whole period of time, while "at the beginning" more literally describes a single moment in time, similar to the difference between saying "in the morning" and "at 8 a.m."

Compare your question to "in the end" versus "at the end." "In the end" is an idiom synonymous with "ultimately." There's a clear distinction. I think the same can be said for "in the beginning"/"at the beginning."

"In the beginning" are the three words that open the Book of Genesis in the Bible. For Christians, the phrase conveys that additional sense of an origination.

"At the beginning" by itself just sounds incomplete to my ear. At the beginning of what?

Firstly, the [pedantic] interpretation of those phrases probably differs between locations and cultures (American English as opposed to British English etc').

Personally, it seems to me that "in the beginning" refers to time and "at the beginning" refers to placement. Often they might be casually interchanged with a figurative allusion to the other meaning.

For example: "at the beginning of the book" ,IMHO, emphasizes more the place [physically] (first pages/chapter etc') while "in the beginning of the book" emphasizes more that it's early relevant to what is happening in the book.

For most uses, I think using 'at' sounds better and I'd be more likely to use it, whether according to what I wrote here or less pedantically.

At the beginning of the book ...

At the beginning of the semester ...

At the beginning of my speech ...

These are all fine and unremarkable.