This question applies to both religion and science.
According to my religion at least, God is subject to natural laws, he did not create all matter in the universe, but instead created the universe by organizing the existing matter in it into planets, stars, galaxies, platypuses, etc, and he himself is composed of the purest matter that had no beginning and therefore will have no end.
Similarly, science currently claims that matter cannot be destroyed, only transformed, and that the smallest particles in the universe cannot be created. Science has never created matter, they've discovered the Higgs bozon, which can give other matter mass, but they've never created a particle out of nothing. Niel DeGrasse Tyson refers to phenomenon like this as "spooky." Everything we can conclude about our universe goes back to the big bang, but the big bang wasn't the origin of matter, some theorize that it was composed of all the matter in the universe that existed previously.
If matter cannot be created, is infinite, and has no starting point, then how does it exist?