In response to no particular post here--
Any Israelite could claim to be a son of God: “Thus says YHVH: Israel is my first born son. I have said to you, ‘Let my son go, that he may worship me…’” (Exodus 4:22-23) And : “You are the children (beni’im; literally “sons”, but the masculine plural applies to mixed-gender groups as well: there is no neuter in Hebrew) of YHVH your God.” (Deuteronomy 4:1)
I am not going to comment on what Jesus said (or is said to have said) or thought. There seems to be no question that the phrases “son of man” and “son of God” took on messianic meanings, beyond their usage as fairly common Hebraic euphemisms, in certain minority circles (e.g., the Essenes, as well as Jesus’ followers). The whole notion of messiah may also have been narrowed and re-formed, from the range of meanings in the Hebrew Scriptures and tradition, in such groups.
If Jesus claimed to be the only one who was the son of God, that would likely have been taken by most Jews as (a) an insulting and delusional bit of hubris; or (b) a claim that put him at the head of a fringe messianic group. If he was heard as claiming (b), then that at least made him dangerous (in the face of Roman occupation), and—depending on how exactly it was heard—in violation of the central Jewish creedal statement, affirming the oneness/wholeness of YHVH.
If Jesus claimed to be the only one who was the son of man, that would likely have been taken by most Jews as (a) a joke—since son of man was a common euphemism for human being; or (b) a claim that put him at the head of a fringe messianic group. Since this claim did not seem to arouse much response, perhaps it was not heard in any special way—but just as a fairly common euphemism of reference.
Whatever people later claim that Jesus meant, including whatever understanding that may have been contributed by Greek thought, has no bearing on what various people of his time and place (1st century Judea and Galilee) would have heard.
Some Jews have seen Jesus as a charismatic Galilean rabbi, who emphasized in charismatic speech the divine “I-am” in every human being as uniquely reflective of the Torah/Logos of God; others have seen him as one more delusional pseudo-messiah; most, perhaps, do not consider him one way or another, and would just shrug if asked. After all, they don’t generally read the NT—and Christian theological categories and forms of Biblical exegesis are so paradigmatically different from Jewish tradition (going back before the time of Jesus) as to be alien to, not just what they think, but how they think about spiritual matters and scripture.