Yes there is evidence that the people of Israel knew they were going to get the Torah prior to Kabalat HaTorah.
Ray's answer cites Shemot 6:7. Even before that, in Shemot 3:12, God says to Moshe
וַיֹּ֙אמֶר֙ כִּֽי־אֶֽהְיֶ֣ה עִמָּ֔ךְ וְזֶה־לְּךָ֣ הָא֔וֹת כִּ֥י
אָנֹכִ֖י שְׁלַחְתִּ֑יךָ בְּהוֹצִֽיאֲךָ֤ אֶת־הָעָם֙ מִמִּצְרַ֔יִם
תַּֽעַבְדוּן֙ אֶת־הָ֣אֱלֹהִ֔ים עַ֖ל הָהָ֥ר הַזֶּֽה׃
And He said: ‘For I shall be with you; and this is the sign for you
that I have sent you: when you take the people out of Egypt, you will
serve God on this mountain.’
Rashi comments on what God told Moshe
דָּבָר גָּדוֹל יֵשׁ לִי עַל הוֹצָאָה זוּ, שֶׁהֲרֵי עֲתִידִים לְקַבֵּל
הַתּוֹרָה עַל הָהָר הַזֶּה לְסוֹף ג' חֳדָשִׁים שֶׁיֵּצְאוּ מִמִּצְרָיִם.
"I have a matter of great consequence dependent on this departure (of the Israelites from Egypt). For they are destined to receive the Torah upon this mountain three months after they leave Egypt."
(based on Midrash Shemot Rabba 3:4)
So at least Moshe Rabbenu knew from the beginning that they would receive the Torah. Did he tell this to the people? see Shemot 4:28
וַיַּגֵּ֤ד מֹשֶׁה֙ לְאַֽהֲרֹ֔ן אֵ֛ת כָּל־דִּבְרֵ֥י יְהוָ֖ה אֲשֶׁ֣ר
שְׁלָח֑וֹ וְאֵ֥ת כָּל־הָאֹתֹ֖ת אֲשֶׁ֥ר צִוָּֽהוּ׃
And Moshe told Aaron all the words that God had sent
him, and all the signs that He had commanded him.
and Shemot 4:30
וַיְדַבֵּ֣ר אַהֲרֹ֔ן אֵ֚ת כָּל־הַדְּבָרִ֔ים אֲשֶׁר־דִּבֶּ֥ר יְהוָ֖ה
אֶל־מֹשֶׁ֑ה וַיַּ֥עַשׂ הָאֹתֹ֖ת לְעֵינֵ֥י הָעָֽם׃ וַֽיַּאֲמֵ֖ן הָעָ֑ם וַֽיִּשְׁמְע֡וּ כִּֽי־פָקַ֨ד יְהוָ֜ה אֶת־בְּנֵ֣י יִשְׂרָאֵ֗ל וְכִ֤י רָאָה֙ אֶת־עָנְיָ֔ם וַֽיִּקְּד֖וּ וַיִּֽשְׁתַּחֲוּֽוּ׃
And Aaron spoke all the words that God had spoken to Moshe,
and he performed the signs in front of the people. And the people believed and they heard that God had remembered the children of Israel and that He saw their affliction, and they bowed their heads and prostrated themselves.