@STT I will give it another try.
First, we accept that there is a first mover, God, the uncaused cause.
Now, this first mover must be all together simple. If it was not, it would be a composite, but a composite is always the result of its parts being moved. Which could not be the first mover, or the uncaused cause.
Now, if God is all together simple, He cannot be moved himself, as anything that is moved is by necessity a composite, so God is not movable, ie He is immutable.
Since time is a result of movement, and God is immutable, he is therefore eternal, ie outside of time. Which is a more proper way of saying immortal.