You brought a package from somewhere in the NCR to New Vegas. Nothing about the story implies you've been a courier and only a courier your whole life. Nothing implies you've even been doing it for longer than the time it took to get from California to Nevada.
Well, you could be right, I'll grant you. But what I'm basing my assumptions on (both our positions are merely that, assumptions), is this (from fallout wiki):
"Not much is known about the Courier's background, apart from they have some sort of a relationship with Ulysses, the previous Courier Six. For reasons unknown, Ulysses pulled out of the delivery job when he learned that the Courier's name was
next on the list, seemingly convinced that the job would kill the Courier - and he was almost right."
I interpret that part about our Courier to mean they were 'next on the company's list of available couriers for a job'. Which to me infers a regular company employee (for an unknown period of time, long or short), waiting for the next available courier job. Of course it may have been their very first job after signing up, but he/she would have had to sign up and become an employee of the company in order to be on their available couriers list. So, I can realistically infer (in my opinion anyway) that the courier was an official company employee, although we aren't told how long they had been with the company prior to the start of NV. But it wasn't like they just hooked up with some random stranger on a street corner in California and said "Sure, I'll take a package to Vegas for ya for XXX caps."
So, I have some basis in the story background to realistically believe that the courier may very well have been employed with that company for more than just the one (almost fatal) job.