Already in תנ”ך, the word מנחה, which means offering or gift, has the connotation of a time of day.

מלכים א יח:כט
וַֽיְהִי֙ כַּעֲבֹ֣ר הַֽצָּהֳרַ֔יִם וַיִּֽתְנַבְּא֔וּ עַ֖ד לַעֲל֣וֹת הַמִּנְחָ֑ה וְאֵֽין־ק֥וֹל וְאֵין־עֹנֶ֖ה וְאֵ֥ין קָֽשֶׁב:

דניאל ט:כא
וְע֛וֹד אֲנִ֥י מְדַבֵּ֖ר בַּתְּפִלָּ֑ה וְהָאִ֣ישׁ גַּבְרִיאֵ֡ל אֲשֶׁר֩ רָאִ֨יתִי בֶחָז֤וֹן בַּתְּחִלָּה֙ מֻעָ֣ף בִּיעָ֔ף נֹגֵ֣עַ אֵלַ֔י כְּעֵ֖ת מִנְחַת־עָֽרֶב:

And it is the afternoon.  When does it take on this temporal connotation?

In Ezra:

עזרא ט:ד-ה
וְאֵלַ֣י יֵאָסְפ֗וּ כֹּ֤ל חָרֵד֙ בְּדִבְרֵ֣י אֱלֹהֵֽי־יִשְׂרָאֵ֔ל עַ֖ל מַ֣עַל הַגּוֹלָ֑ה וַאֲנִי֙ יֹשֵׁ֣ב מְשׁוֹמֵ֔ם עַ֖ד לְמִנְחַ֥ת הָעָֽרֶב:  וּבְמִנְחַ֣ת הָעֶ֗רֶב קַ֚מְתִּי מִתַּֽעֲנִיתִ֔י וּבְקָרְעִ֥י בִגְדִ֖י וּמְעִילִ֑י וָֽאֶכְרְעָה֙ עַל־בִּרְכַּ֔י וָאֶפְרְשָׂ֥ה כַפַּ֖י אֶל־ יְקֹוָ֥ק אֱלֹהָֽי:

However, it is entirely possible that in this case the verses actually refer to the מנחה offering in the evening, rather than simply specifying a time of day.  Furthermore, מנחה is explicitly modified by הערב, indicating that מנחה alone would not be sufficient to specify the time of day.

From W.F. Albright’s review of Textes accadiens des archives sud (archives internationales), by Jean Nougayrol in BASOR (Bulletin of the American Schools of Oriental Studies), 146 (1957) p. 35:

Another new point is in No. 19. 55, where the word manahatu is scarcely the plural of Accadian manahtu, “toil,” but is rather the plural of the noun which appears as minhah, ” gift, offering,” in Hebrew, m(a)nhitu as a loanword in New Egyptian with the same meaning, and mnh, probably with the same sense, in Ugaritic (from the secondary derivative mnh, ” to give, bestow,” found also in Arabic). With this meaning the text acquires new importance for the practices governing relations between reigning princes in Syria during the thirteenth century B. C