When was Ecclesiastes written?

Traditionally the book of Ecclesiastes has been assumed to be written by King Solomon as a later reflection of his life as hw comes to a near end. This sounds good but the fact is that the content of Ecclesiastes sounds like Greek fatalistic speech in that the and its late arrival as in terms of other wisdom/poetry books as we have evidence of all others in some shape or form before the exile (The Rose Publishing Bible Overview says this about the date, “If it was a later author, most scholars believe it was written after God brought the Jews back from exile (after 539 BC)”. In fact I somewhat agree with the liberal view that Ecclesiastes was written post-exile and was attributed to Solomon, as it is done with the other chapters of the Song of Songs (it is assumed that Solomon wrote the first chapter but other’s are unique and just got added into one whole text over time). Richard S. Hess in his book “The Old Testament: A Historical, Theological, and Critical Introduction.” says this about Ecc.
“Although the issue of cannon was discussed at the beginning of this survey (see introduction), it becomes important for understanding this book due to the unusual dispute concerning the place of Ecclesiastes, more than that for most other books of the Bible. Its appearance among the scrolls of the separatist Qumran community as early as the mid-second century BC suggests an acceptance in the intertestamental Judaism. Questions arose due to some apparent contradictions in the book (cf. 2:2; 7:3; 8:15), a fatalistic view of life (1:3; 11:9), and the pessimistic nature of the work regarding belief in God.”
So, my question is this, if Ecclesiastes was written post exile, is it possible that it was influenced by Hellenistic cynic thinking of the time and made by a ground of Hellenistic Jews?