Re: How soon after the Big Bang would there be elements for life?

Sorry for the delay in answering this question but I have been giving it 
some thought. The message that you provided has some assumptions in it. 
First of all, all elements in all things are a consequence of the big bang. 
In the energy burst that is the big bang, after about "three minutes" as 
Steven Weinberg would put it, the synthesis of all of the protons and 
neutrons was complete. Since all elements are made of these constituents, 
arguably, the conditions for life existed right away.

But that is not really what you are asking. Again according to Weinberg 
(Steven Weinberg, "The First Three Minutes", BasicBooks, 1993) it took 
about 700,000 years after the big bang for the Universe to cool 
sufficiently that protons and electrons could come together. Prior to that, 
the Universe was not transparent to radiation. Of course, there was no 
Earth and no "year" and time might have been doing some funny things but 
call it just under a million to get the first atoms started. But simple 
atoms existed and could start the process of star formation.

The first galaxies, stars, and Super Novae took another billion years to 
form. That is, the latest deep space evidence would suggest that galaxies 
existed a billion years after the big bang. And that these galaxies were 
whirling maelstroms of matter. The rate of star production was at least an 
order of magnitude faster than today and may have been several orders of 
magnitude faster. And the big stars burned fast, producing many more super 
novae then than today. As nucleosynthesis inside a single star can and does 
produce the higher elements (carbon through to iron), then a billion years 
or so after the big bang, the elements necessary for the formation of 
planets and living organisms could have been present in the Universe.

Of course, would there be enough? How did the elements get together to form 
a planet? The questions around how the solar system formed and how did we 
get planets follow a variety of models. Gravitational collapse of the 
interstellar mass of hydrogen and other elements is the basic answer. But 
what started the gravitational collapse? Maybe another super nova? The 
elements that form the planets (and all living organisms that we know 
about) did not need three super nova to produce them. A single star could 
do that (although it is likely to have gone through multiple episodes of 
mass production/ejection as the nuclear fires progressed from hydrogen to 
helium to heavier elements - may be this is what you are referring to when 
you say "three super nova"?) but a single star would eject its matter at 
some fraction of the speed of light away from itself. To get this matter 
together to form planets would require that the atoms slow and congregate 
to form a second generation solar mass. Realistically, this would require a 
few more billions of years. Indeed, in the case of the Sun, this only 
happened 5 billion years ago - about 9 billion years after the big bang 
(depending upon which date you use for the start of the Universe!). 

So, in answer to your question, about 700,000 years for the first atoms, 
another billion for the first generation of super nova and heavy atom 
synthesis, and another couple of billion for the first planets with the 
requisite elements for life. All told, 3 to 5 billion years after the big 
bang there could have been the possibility of life - although the only 
example that we actual know about took about 9 billion years to get to the 
point where life could form. 

Hope this helps.