It would seem to me that an infinite series of contractions and expansions of the universe would be equally amenable to the existence of God as would the Big Bang. Of course both ideas are difficult to get your head around.
...infinite series of contractions and expansions...
When did this series begin?
The Bible says in Genesis 1 that creation occurred one time (in six days) and God rested on the seventh day.
It also says in Revelation 21 that at the end of the world (at the conclusion of Christ’s millennial reign) God will create a new heaven and new earth. And here the servants of God shall reign forever and ever.
No infinite series. There are marked phases: Creation ex nihilo, rest, fall, atonement, incarnation, death-burial-resurrection, return, resurrection unto life, resurrection unto damnation, consignment of death and hell to the lake of fire, new heaven and earth, eternal reign with Christ.
Which god do you speak of? Certainly this statement is not true of the Judeo-Christian God, whom I worship. He revealed in Genesis 1:1 "In the beginning, God created the heavens and the earth." None of this oscillation or cycling. Those are Buddhist ideas.