For example the entire atomic composition of the stars in the observable universe depends exquisitely on the expansion parameters at the big bang. The ratios can be traced back through the expansion to the quark-gluon soup stage. Changing the expansion rates changes the delicate balance between the particles that form at that stage, and when the various particle fractions "freeze out" during expansion when the temperature cools (btw we're talking about seconds from the big bang here :) which can be subsequently observed in stars all over the universe by spectroscopy. It's pretty beautiful.

There are so many intricate dependencies between these pathways that it's pretty unrealistic to postulate anything else than a big bang + cooldown process IMHO.