That's a hard question to answer because it really depends on the filmmaker's financial situation. When making my first indie documentary I could not possibly imagine treating it like a full time career. How could I? No one was giving me any money to make this film and if I spent way too much time on this project I had no time left to make money from a regular job and feed myself. Often the first film and many times a second one, is made on a shoe string budget. You can't afford to hire anyone and you can't pay yourself so the effort comes from time left over from whatever you are doing to pay your bills.
But I can never accept calling filmmaking a hobby. A hobby is something like an activity you do on the weekends or in the evening when you have a couple of hours to kill. Filmmaking is much more involved and demands so much more from you.
From the time you have a film or documentary concept and launch yourself into this pursuit, it becomes an all consuming endeavour. You become obsessed and really everything else falls in the realm of banal chores which you must do to live but pretty much 24/7 the idea of the film and how to get it done takes over.
So when does filmmaking become a career? You can have a career within filmmaking in roles such as camera person, editor, sound operator or actor etc. Most of these tasks offer good and lifelong careers opportunities especially with established studios and companies but ofcourse this cannot be mistaken for filmmaking. The difference is that it is not your vision you are working on. If you want to own the film, you have to make it thus be prepared to take charge and provide all resources necessary to get the film done. That is why filmmaking is a hard career to pursue, but many indie filmmakers have gone onto make not only their first rookie film but many others thereafter carving out a voice for themselves and a very lucrative and fulfilling lifelong career. Michael Moore who made Bowling for Columbine is one such person. I challenge you to look up other such success stories and find out how they were able to get their first film made!