I would go with "empezar desde abajo" which means to start in a low rank position, and then escalate because you are supposed to be good at what you do.
"Derecho de piso" rather means to be the newbie (could be in the office, the gym, school or any other group of people) and doing the things no one else wants to do, and you have to deal with it until you are no longer considered the newbie.
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mmm...jamón.
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