Firstly (see what I did there?): No. Firstly can't be used in the same meaning as at first or initially. As @deadrat mentioned, "firstly" meaning first is restricted to enumerations, so the initial observation of muons would be the first time.
Secondly, depending on the context of the text, the use of firstly in the excerpt you've given us may be correct after all (though with an incorrect word order). But I only consider this option because I read a lot of scientific papers and I know that grammar and writing isn't their (scientists) strong suit. I assume it should indeed be first, but I'll expand on my reasoning:
If the text is about how muons were originally observed for the first time ever, then yes, it should be first.
However, if the context of the text is different (i.e. it talks about how muons were observed in an experiment), then firstly could be correct. But only if it's followed by additional ways muons were observed. As I mentioned before, I only consider this because I know the grammar in a lot of scientific papers is horrendous. The only context I would accept firstly in would be:
"muons were observed firstly in cosmic rays, secondly in radioactive decay, [...]"
And that is assuming that the author of the text isn't great at grammar (which on a whole, they are not). The excerpt you've given is too short to be sure what the author meant.
So in short: firstly is only for enumerations and if the context of the paper meant it in that way, then the phrase you have shown us is gramatically incorrect (word order), but experience has taught me that in scientific papers, both of these options (incorrect use of firstly or just an incorrect word order) are possible.
PS: Thank you @FumbleFingers for pointing out I wasn't very clear in my reasoning behind my consideration of the second (though gramatically incorrect) option.