I only wished to refine your "4 to 6 billion years" estimate

The early universe formed only stars of hydrogen and helium. Those stars had to go through a life cycle to produce heavier elements in their supernova destructions. Those heavier elements had to rejoin into second generation stars, and that was the earliest that solid planets could form. Those planets formed of smaller pieces of solid matter called asteroids (chunks of rock in space formed themselves by accretion in the second generation star disk). The oldest of those are about 4.5 BY, suggesting that to be the earliest that solid planets could form.

Of course, in fantasy, anything you want to be true can be ....