1. All the big bang cosmology, and the inflationary scenario, depends on how we might model, in a physical sense, the emergence of something from nothing. The idea is that as the world cooled down from the big bang, there emerged orderliness, much as cooled water becomes crystalline ice. That orderliness is the something that arises
2. There may be speculation about before the big bang, but in general physicists see time as something denominated by events (not by an external clock), and before the big bang there was no time.
3. As for living matter, it is likely that we will find matter that exhibits various levels of what we would call living. In other words, the living-ness was not a single step, but more likely was a series of incremental steps. Non-living matter surely on its own develops in this way, but it is unlikely that there was a single step that divided time into before living and after living.
4. As for organic matter developing cognition and information processing capacity, we find that there are many steps along the way, and different living matter displays various degrees of consciousness etc. Much like #3.
5. Being living matter that is conscious, cognitive, and information processing, is an ongoing process. It has not stopped with current mankind. It's not that we will come to see the current era as being only half living and half-dumb. Rather in millennia new steps will be developed.