It is indeed a cool idea, but it is likely completely wrong.
For life, it is not enough for the ambient temperature at the surface of a planet to be acceptable.
For life to appear, it is necessary that the interior of the planet is much hotter than the surface, so that this thermal non-equilibrium will be converted into chemical non-equilibrium by volcanism.
When the universe had cooled to a habitable temperature after the Big Bang, if any celestial bodies existed they were in thermal equilibrium, so they could not provide any energy for the appearance of life.
The internal heat of a planet normally has 2 sources, the radioactive decay of heavy elements that have been produced only in catastrophic events that have happened late in the history of Universe, e.g. supernova explosions or neutron star impacts, and the residual heat produced from collisions with other planets.
For satellites close to big planets or for planets close to stars there may be also heat produced by tidal deformations.
Such sources of heat are unlikely to have existed in the early Universe, and even supposing that collisions could have existed, in that case the environment with a life-enabling temperature would not have been correlated with the epoch when the entire Universe had a temperature that now is suitable for life.
Moreover life cannot appear without chemical elements up to the iron-cobalt-nickel group, which are the chemical catalysts on which life depends as much as on the structural elements HCNOS.
The iron group elements are generated only late in the lifetime of a star, so life can appear only in celestial bodies that recycle matter from explosions of the first generation stars, billions of years after the Big Bang and long after the Universe had cooled.