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I think that the term "a pri·o·ri" might apply here. My premise that the the universe has always existed, and so space too has always existed. I see no reason to think that space hasn't also always been infinite.
Theoretic deduction is reason without facts. I thought that's what exactly most scientist wanted to avoid.
And besides, if you believe the universe always existed, you don't believe in "an origin" of all matter.