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What the hell does general relativity have to do with "intelligent design"?
"There is no evidence for intelligent design. The laws of physics and chemistry, and Darwinian evolution, are sufficient to account for everything in the universe." Steven Hawking.
“It was, of course, a lie what you read about my religious convictions, a lie which is being systematically repeated. I do not believe in a personal God and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it.” Albert Einstein. Nor did he believe the universe was designed for us.
Space-time and what we refer to as the universe may have begun at the Big Bang and expanded from there, but the universe existed prior to that expansion. Time may begin at a certain point, the universe as we know it may begin at a certain point, but current modeling is unable to investigate the universe outside of time, so there's no certainty it has a beginning at all.
And yes something can come from a vacuum, see quantum electrodynamics.
And no "intelligent design" will never be a scientific theory even if you tag the word theory onto the end you will still be nothing more than a cdesign proponentsist. It's not a new idea, it's an old idea repackaged.