Actually, just about everything in the universe is 3 in 1. Not just space.
That’s an interesting line of thought; but I think readers in Paul’s audience would have been more familiar with Judaism’s emphasis on the number 7 (as in the 7 days of creation) or Pythagoras’ theory of number which emphasized all the numbers up to 10. (I’m not saying Paul followed Pythagoras, just that this was an intellectual framework that would have been familiar to his readers if they were thinking of the universe in terms of number.) Personally I think all numbers reflect God’s glory in one way or another. For instance God is One; the image of God is created male and female in Genesis; we have the Trinity and other instances of three as you mention; the four four-faced cherubim seen by Ezekiel; the twelve tribes of Israel; the 144,000 servants of God in Revelation; etc. George Ferguson’s “Signs and Symbols in Christan Art” has a bit on Christian number symbolism in Chapter 11 that’s an interesting read.