I don't know how google 2FA is implemented, but I'd just assumed the initial code is akin to something like an initialisation vector / nonce for a counter or CBC mode block cipher. With the counter being 'time', meaning the scheme works something like:

hash_fn(concat(IV, time)) -> func(somehash) -> [code seq. 1]

Then on the next round the IV is discarded and it becomes:

hash_fn(concat([code seq. 1], time)) -> func(somehash) -> [code seq. 2]

That's almost certainly an over-simplification / wrong; it doesn't seem very secure to just use the previous output as the IV for the next round. Maybe it chains all previous outputs together somehow, IDK. I should probably research this, given how much I rely on 2FA for security.

EDIT: The Wikipedia article on TOTP seems to suggest that you're right; the initial shared secret looks indistinguishable from a password (although the article is a bit vague): https://en.wikipedia.org/wiki/Time-based_One-time_Password_A...