You appear to misunderstand the meaning of the terms "inconsistent" and "incomplete" in the context of Gödel's theorem.

"Inconsistent": There is at least one statement within the system that can be proved both true and false.

"Incomplete": There is at least one statement within the system that is true, but cannot be proved to be true within the system.

Since Gödel's theorem applies to formal systems in mathematics, it does not say anything about the possibility or impossibility of constructing a "complete" (whatever that means) mathematical description of our reality.