In the written NT, "the son of man" is "ο γιος του ανθρώπου," with a definite article "ο." This would presumably be a Greek translation of an Aramaic phrase used during the apostolic period (unless a Greek-speaking evangelist invented its usage as a title out of whole cloth), and would have been familiar to first-century Palestinian Jews as a stock phrase heard in readings of the then-oral targums (e.g., Daniel 7:13).
I don't know any Aramaic, but I gather that in Aramaic this is "bar enos," and as far as I can tell from looking at a description of the grammar, the meaning that is conveyed in English or Greek by a definite article is indicated in Aramaic by a suffix "-a."
So if an Aramaic speaker wanted to say "the son of man," would they have said something like "bara enos?" Or would the "-a" go away because of the following vowel or something like that?
The point here is whether there would have been any distinction apparent in oral Aramaic between "[a] son of man" and the title "the Son of Man." (I gather that Koine Greek had definite articles but no indefinite articles.)
Some linguistic information about the phrase in Aramaic: https://www.goarch.org/-/the-aramaic-phrase-bar-enos-son-of-man-dan-7-13-14-revisited