When the president-elect becomes inaugurated, does his cabinet picks take office the same day too?

They don't start until they get confirmed by the Senate.

Quote from bethesda

When do you think they'll get confirmed?

They only just started the Senate hearings this Tuesday with Pete Hegseth kicking things off. After the hearings, the specific committee (In Pete's case the Senate Armed Services Committee) has to vote to approve the candidate to be presented to the senate for a vote.