The space within and between solar systems was quite warm and capable of supporting liquid water.
There might not have been enough time during this period for intelligent lifeforms to develop, but a large stew of amino acids and other building blocks of life could have developed during this period.
Those building blocks could have hopped rides on meteorites and asteroids which eventually bombarded the Earth providing it with water and the beginnings of life.
This explanation seems to ignore the likelihood that God spoke life into existence.
As in speaking some sort of language.
(Fascinating, how the genetic code is a form of language.)