Wikipedia places the philosophical root of the "Turing Test" with Descartes. Clearly Descartes is incredibly valuable in this regard, and also in regard to "cogito ergo sum", which can be applied to automata that perform calculations, as a basic condition in the overall philosophy of artificial intelligence.
But it seems to me the concept of the thresholds that constitute Turing Tests originates with Protagoras, who proposed that "Man is the measure of all things."
Full quote may be translated as: "Of all things (used by man) the measure (of these things) is man: of the things that are, that they are, of the things that are not, that they are not."
(Apologies as I cannot find a direct link for the Greek online. I re-translated the first part of the proposition for clarity, but lifted the second part from Bostock, whose Ancient Greek is undoubtedly better than mine, because it is potentially ambiguous, even in the original, and Bostock's interpretation makes good use of that ambiguity.)
χρημάτων "things" is distinct from ὄντων "things", which is interpreted to mean Protagoras was speaking about things that man has a direct relationship to, such as property, tools, affairs and so forth. "A thing that one needs or uses" is listed in the LSJ.
Protagoras can unquestionably be extended to AI, which are tools.