>If so, what would be the magic ingredient that saves human brains from immediacy? It can't be memory, because Turing machines have memory as well.

The universe is not deterministic. There is one brain state at time T, but at time T+1 there are many possible brain states, all with different possibilities. What determines which state at time T+1 the consciousness at time T perceives itself as progressing to? If we define this as a function, which associates states at time T with states at times T+1, then this function loosely fits the definition of "free will". We can't actually construct this function or say anything about it, but we can say it can't not exist (as consciousness perceives itself as progressing to a single future state), which by the law of the excluded middle implies it must exist. The definition doesn't however prevent it from essentially being completely random.