Von Neumann said: "In mathematics you don't understand things. You just get used to them."
For practical purpose of getting the completeness theorem to click, my advice would be to stop thinking about it and instead just use it in a bunch of proofs. The way you use it in the a proof is you say something like "...and since, as we've just shown, this sentence phi is true in all structures for the language, it follows that there is a proof P of phi, and therefore..."
If writing such proofs isn't the sort of thing you want to do, then you almost certainly don't actually need to know Goedel's Completeness Theorem, which is a highly technical theorem whose philosophical, epistemological, metaphysical, mystical, and magical applications are all completely overblown by people who want to sell books.
For practical purpose of getting the completeness theorem to click, my advice would be to stop thinking about it and instead just use it in a bunch of proofs. The way you use it in the a proof is you say something like "...and since, as we've just shown, this sentence phi is true in all structures for the language, it follows that there is a proof P of phi, and therefore..."
If writing such proofs isn't the sort of thing you want to do, then you almost certainly don't actually need to know Goedel's Completeness Theorem, which is a highly technical theorem whose philosophical, epistemological, metaphysical, mystical, and magical applications are all completely overblown by people who want to sell books.