[CaptainNegative]

> Since P is a subset of NP, everything in P can be also be turned into an instance of SAT.

This statement is kind of trivial. The same is true for any language (other than the empty language and the language containing all strings). The reduction is (1) hardcode the values of one string, y, that is in the language and another string, z, that is not in the language (2) solve the problem on the given input x in polynomial time poly(x) (3) return y if x is to be accepted and z otherwise.

The total running time is at most poly(x)+O(|y|+|z|) which is still poly(x) since |y| and |z| are hardcoded constant values.