I wondered what’s the first evidence that the Jewish people believed in the concept of Mashiach (the figure of the Messainic era/age)?
Of course there are well known scriptures referring to Mashiach, but there needs to be a point where we started to identify them as such. So what’s the first reference we can find in Jewish literature of this believe?
Written literature held sacred by the Jews include the book of Genesis, which existed prior to the the complete Chumash. The complete Pentateuch was written in 13 scrolls by Moshe at the end of his life, but Genesis and the first part of Exodus was written by Moshe prior to the reception of the ten commandments (see mechilta and Rashi on Exodus 23:7).
The first words in Genesis, about God’s spirit moving over the surface is a veiled reference to Moshiach. Every word discussed at the beginning of Creation, describes events of world history and how it reaches towards Hashem’s plan for His creation. One important juncture in fulfillment of his will is the period of Moshiach.
Another more explicit reference in the text itself is found when Yaakov discusses his vision of the end of times with his children on his deathbed and offers each one a blessing informing them of their specific strengths. When he addresses Yehuda he talks about the monarchy emerging from his descendants until the time of tranquility or until Shiloh comes. This is understood by many as reference to Moshiach.
Your interest to find the first evidence is a bit vague. I am not sure if you are referring to a documented literary source or historical episode as related in our oral traditions or perhaps something else.
Please share the focus of your interest, your own research and motivation to learn more about this in the comments and perhaps someone in the administration can be more helpful to you.
I hope these sources are helpful.