(this includes most inflation cosmologies). .. Time didn't exist apart from the big bang.
I thought 'inflation' is well-established and what we do not know are events prior to 'inflation'. Big Bang is prior to inflation and whether time existed at that time or not is not answerable today. Our knowledge starts only after 'inflation'. I have no problem with 'Ex-nihilo' if science finally gravitates to that. Our books (RigVeda) too speculated on what existed when there was no time more than three thousand years ago.
Book 10. Hymn CXXIX. Creation.
1. THEN was not non-existent nor existent: there was no realm of air, no sky beyond it.
What covered in, and where? and what gave shelter? Was water there, unfathomed depth of water?
2 Death was not then, nor was there aught immortal: no sign was there, the day's and night's divider.
That One Thing, breathless, breathed by its own nature: apart from it was nothing whatsoever.
3 Darkness there was: at first concealed in darkness this. All was indiscriminated chaos.
All that existed then was void and form less: by the great power of Warmth was born that Unit.
4 Thereafter rose Desire in the beginning, Desire, the primal seed and germ of Spirit.
Sages who searched with their heart's thought discovered the existent's kinship in the non-existent.
5 Transversely was their severing line extended: what was above it then, and what below it?
There were begetters, there were mighty forces, free action here and energy up yonder.
6 Who verily knows and who can here declare it, whence it was born and whence comes this creation?
The Gods are later than this world's production. Who knows then whence it first came into being?
7 He, the first origin of this creation, whether he formed it all or did not form it,
Whose eye controls this world in highest heaven, he verily knows it, or perhaps he knows not.
I realize, we do not seem to have not progressed much in the next three thousand years.
Nasadiya Sukta, writer: Prajapati Parameshthin (my homage to him), Translation by Ralph Griffith
http://www.sacred-texts.com/hin/rigveda/rv10129.htm