No, President Washington was the first President of the United States. He was elected to the position by the congress that was established at the time. Also, Pres. Washington put the "so help me God" into the oath of office, due to him not knowing what was going to be in store for the newly founded nation. He also refused to be called king when congress wanted that to be the title here as it was in the mother country of England.
You are correct about him being the first CiC of the US. He held that position when the continental armies agreed that he was the best suited to lead all battles against the Brits. He held that title until the war was over. At that time he became the first president.