We know the universe began to exist because all the scientific evidence, like the Big Bang and the second law of thermodynamics, points to a beginning, and philosophy shows you cannot have an actual infinite past. God exists in the sense of being the necessary, immaterial, timeless cause of the universe. He is not made of matter or bound by space and time. As for evidence of an eternal consciousness, the fine-tuning of the universe, the origin of information in DNA, and the existence of objective moral values all point to an intelligent, personal source rather than blind, unconscious forces

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"The existence of objective moral values"? Where do they exist? What are they made of? "Philosophy shows you cannot have an actual infinite past" How does it do that? How does DNA or physics indicate an "intelligent, personal source"? In what way does the second law of thermodynamics point to a beginning? The Big Bang and 2nd law of thermodynamics are not "scientific evidence", but rather theories to explain actual scientific evidence (eg galaxies drifting apart or heat radiating from a hotter to a colder region). That actual scientific evidence does little to prove that there was a definite beginning. If things are spreading apart now, then in the past they were probably closer together, but this does not show that if you just extrapolate all the way back to when everything was (presumably) really close together that nothing happened before this moment or that this moment ever actually occurred.