Nucleii are there at 35 minutes, it's 700,000 years before atoms come about.
http://csep10.phys.utk.edu/astr162/lect/cosmol ogy/hotbb.html
But with the analogy of 24 "hours" between the BB and now, I make that 0:00:04 am.
The issue of what changes would still give us an inhabitable universe is interesting.
We don't know how the various constants and laws came about. So we don't know which if any are dependant on each other so what looks like a fabulous coi-incidence might not be.
The other thing is the issue of other possible universes which might be totally uninhabitable, ours then looks special because it's the only one we can see.
This is what's known as the weak anthropic principal. The Idea that the universe must be just so In order to create us is the strong anthropic principle and is somewhat debatable, however you do have to consider it in the context of quantum mechanical ideas and it's not quite as absurd as it might at first appear.
I don't know which thesis Heathfield read that said that the Universe got more and more complex - but it does seem to fly in the face of ideas such as thermo-dynamics and Entropy!