"You are My Witnesses"
The "Aseret HaDibrot," the Ten Utterances, or Commandments, of G-d to the Jewish People, begin "Anochi Hashem Elokecha Asher Hotzaticha Me'Eretz Mitzrayim Mi'Bait Avadim", "I am the L-rd your G-d, Who brought you forth from the Land of Egypt, from the House of Bondage." A famous question is asked, "Why did they not begin with the even more impressive accomplishment of G-d; namely, the Creation of the Universe?"
The RAMBAN answers that the reason is that the Creation was an event which had no human witnesses. Therefore, it would be only by an act of pure faith, truly a "leap of faith" that would be required for someone to believe that the Universe was created by a Divine Being at some moment in the past. Whereas, the Exodus was an event, or series of events, that had millions of witnesses; namely, the people of Israel. Their eye-witness testimony was passed from parent to child down the generations. This continuum of generations is part of what enables us to relive and re-experience the Exodus on the night of the Seder.
This event, together with its follow-up, so to speak, the Revelation of G-d on Mount Sinai, where He gave the Torah to the Jewish People, provided indisputable proof of the Existence of a G-d Who had not abandoned the World after its Creation. Rather, the transmission at Sinai showed that G-d had very definite ideas as to how the affairs of those who live in it should be conducted. The gift which He had given the Jewish People would ultimately enlighten and illuminate the world, with its G-dly way of life.
The Exodus had also shown that G-d was the Omnipotent Ruler Who could overthrow nations and their so-called gods effortlessly. Also, that He could temporarily suspend Natural Law (since He had installed that System of Law in the first place), as He did during the Plagues and when He split the waters of the Sea of Reeds.
Additionally, starting from the premise that G-d had delivered Israel from Egypt, displaying infinite might and infinite caring, as the Aseret HaDibrot do, one might infer the fact and truth of the Creation.
As the RAMBAN says, "His taking them out from there implies His Existence and His desires concerning the world, for it was with His Knowledge and Direction that we left that place. And it also implies the fact of Creation for if the Universe were Eternal (i.e. it always was as it is now), nothing would ever change from its natural tendency. And it implies His Power; and His Power implies His Unity, as it is written, 'in order that you know that there is none like me in all the Earth.' "
However, given the premise of Creation, one could never have inferred G-d's Involvement with the World, and Willingness to Intervene in the affairs of Man.
In the Book of Yeshayahu, which is the source of the expression "And you are My witnesses," we hear an echo of the "Dibrot," the Utterances, and find support for the RAMBAN, in the use of the word "Anochi," I, the first word of the Commandments, three times:
"I (Anochi is the word used), even I (Anochi), am the L-rd, and no one beside Me is a Savior. I have spoken (at Sinai; within the parentheses is my commentary), and saved (at the Sea of Reeds), and made known my greatness (in Egypt), and there is no stranger among you (who did not experience these events in your collective, historical memory). And you are My witnesses, says the L-rd, that I (Anochi) am the Almighty." (Yeshayahu 43: 11-12)