Welcome to PF,
you are correct, the Earth and Moon did not start out as mutually stationary.
In general, any randomly accreting body will end up with a net angular momentum which means it will rotate so the general circular-ish motion of bodies in the solar system is built-in as a consequence of how it was formed. You can easily see that two bodies approaching and then holding together, unless they happen to have equal and opposite momenta, they won't end up stationary, and, unless they hit exactly head on, they will end up turning about their mutual center of mass.
In terms of Newton's 1st Law, however, the Moon is not in uniform motion ... it is accelerating under the unbalanced force of gravity ... see Newton's 2nd Law. By Newton't 3rd Law, the Earth also orbits the Moon.