I believe that conditions at the beginning of the universe are fundamentally different from those at the end.
The beginning was a very smooth and uniform environment. The end (if the universe collapses) is expected to be lumpy and nonuniform.
In Tipler's theory, it is actually necessary for the ending of the universe to be specially engineered to be as nonuniform as possible in order for infinite computations to exist. The universe must be put into a series of shape oscillations, alternately contracting/expanding along different directions. This shear phenomenon causes energy differentials to continue to exist, which can be used to power computation. Unless life is able to direct the universe into this specific, unnatural pattern of collapse, the universe becomes uniform and nothing more happens.
This would seem to indicate that the early universe, despite being exceedingly hot and dense by our standards, was not a good environment for evolution. Without energy differences there is no way for life to exist.