Is space finite, or is the universe infinite?

Yes, the space we see is finite. When God created out of nothing, he created something, and if it exists it is a something, and if it is a something it is physical, whether gas, liquid, solid, plasma or quantum particles. And if it is physical it has to be finite; it cannot be infinite. So there is no infinite universe. The old steady-state theorists said the universe was infinite and unchanging, but they knew that was wrong and had nothing to replace it until the Big Bang was invented. Yet if you press the Big Bangers on where their singularity came from, they say another universe, and where that came from, another universe, an infinite regress that gets you nowhere. Only God is infinite.