Also remember the Eye has a sort of intelligence, enough to create a signal for the Nomai to follow for the sole purpose of triggering the events that would lead to you finding and entering the Eye.
And it didn't just use the Nomai to do this because it was...too early, I suppose? The eye wanted me to find and enter it at more or less the exact moment of heat death so as to maximize life, and going too early would almost be a waste of time?