Through two millennia the Song of Solomon was interpreted by most Jewish and Christian scholars as an allegory of God's relationship with Israel, or Jesus' relationship with the church. Only lately has the scholarly opinion shifted toward the literal approach. Do the many detailed physical descriptions in the Song of Solomon prove that it was meant literally, or is there another explanation for them? Or are there any other arguments against the allegorical interpretation?
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The traditional allegories are anachronistic. So, if you accept the text as a product of human effort, it's not one of them. I'm unaware of anyone who has ever argued that it was written (in the ordinary sense) by a person intending an allegory -- that is, an allegory that made sense to someone reading at the time. The Christian version wasn't going to emerge without divine assistance from the pen of Solomon, for example.
Thus, I don't think your question is answerable in the frame of discussion here. The allegory arises as a doctrinal interpretation, not in response to the internal evidence of the text, or comparable texts from ancient Near East.
'Prove' is about truth, and this site isn't about truth. None of us 'critics' can prove that G-d didn't dictate the text, and none of you non-'critics' can 'prove' the contrary, if by 'prove' you mean 'by adducing evidence other than the evidence of things unseen'.
There is, however, some ambiguity as follows. The text walks, talks, and quacks as a set of love poems. Period (textually speaking). However, someone, some persons, decided to canonize it. In point of fact, some Jewish persons. We can't know what they were thinking; they've left no evidence. Did they canonize because these poems were attributed to Solomon, and that was good enough for them? Or did they canonize because an allegory had been traditionally attached to them at some point in the past? Or did they canonize because they thought of the allegory on the spot? We don't know. So a sort of middle ground is that some (more or less divinely-inspired person(s)) took these poems, edited them, and canonized them with allegorical intent.