Kurzgesagt just posted a video that speculates that life was possible every where when the entire universe was at the temperature range of liquid water as it cooled after the big bang.
Contradictory evidence might be the establishment of proto-genetic sequences which are capable of encoding at least simple proteins, and some evidence that the development of such capabilities in a biologically-naive environment (that is: without any competition from existing life forms) is more rapid than subsequent evolutionary development. A key concept that needs to be kept in mind when considering the evolution of any system --- biological, technological, informational, etc. --- is that primordial species and forms need not be competitive against any current exemplars with which we're familiar, but only those which exist in their own contemporaneous environment. It's a lot easier to get started when things are just getting started....
I do note that the idea that the entire Universe on average was within the Golidlocks temperature zone might well also mean that localised places and times were subject to vastly greater levels of ionising or other radiation which would be highly disruptive to life.
That said ... the idea that conditions suitable for biological activity literally once pervaded the Universe and are now only found in very localised circumstances orbiting a small subset of stars and limited to rocky planets with significant water ... is both epic and poetic. Literally sparks fading from an all-encompassing explosion....
The main source for the hypothesis appears to be:L Loeb, A. (2014): "The habitable epoch of the early Universe". International Journal of Astrobiology, vol. 13, 4."
<https://www.cambridge.org/core/journals/international-journa...>
Additional sources: <https://sites.google.com/view/sources-big-bang-life/>
Which somewhat takes the shine / bloom off this for me.