In the present day United States Navy, one can enlist without selecting or being assigned a specific rate. These Sailors are considered undesignated or non-rated, Sailors; my understanding is it's formally known as the Professional Apprenticeship Career Track (PACT). Once a Sailor has figured out what rate they want to progress their career in, they "strike" for a rate and work towards getting qualifications to be designated in that rate. Please correct me if I am missing anything.
That said, and how it relates to this forum, can a Crewman in Starfleet, enlist without choosing the technician field they want to be in (like what is in the Players Guide in the ICON system)? If so, have we seen these Crewman onscreen before? What do you image their early career would be like? Have you had characters, or players, in your game(s) who were undesignated Crewman?