Rambam: Shemot: The Appointment of Moses
Thus, those to whom Moshe was sent witnessed his appointment as a prophet, and it was not necessary to perform another wonder for them. He and they were like two witnesses who observed the same event together. Each one serves as a witness to his colleague that he is telling the truth, and neither has to bring any other proof to his colleague.
Similarly, all Israel were witnesses to the appointment of Moses our teacher, at the Revelation at Mt. Sinai, and it was unnecessary for him to perform any further wonders for them.
This concept is alluded to in the interchange between God and Moses at the revelation of the Burning Bush. At the beginning of his prophecy, the Holy One, Blessed is He, gave him the wonders to perform in Egypt and told him, “And they will listen to your voice.” (Exodus 3:18)
Moses, our teacher, knew that one who believes in another person because of signs has apprehension in his heart, and that he has doubts and suspicions. Therefore, he sought to be released from the mission, saying,”They will not believe me.” (Exodus 4:1) Until the Holy One, Blessed is He, informed him that these wonders were intended only as a temporary measure until they left Egypt. After they would leave, they would stand on this mountain and all doubts that they had about him would be removed.
God told him, “Here, I will give you a sign so that they will know that I truly sent you from the outset, and thus, no doubts will remain in their hearts.” This is what is meant by, “This will be your sign that I sent you: When you take the people out of Egypt, you will serve God on this mountain.” (Exodus 3:12) Hilchot Yesodei HaTorah 8:2