There are a couple of different challenges there. In a way it's the chicken-and-egg paradox. First, if you're doing a regular apprenticeship program you have to get the job first, but how do you get the job if you're not an apprentice? In certain trades that's going to be easier than in others, but for the most part you have to start off as a bit of a go-getter to get the job first, and then sign up as an apprentice with the ministry, and then continue on.
In a lot of trades there are alternative programs through which you can take a pre-apprenticeship course at a college or even sometimes a high school to give you the base-level skills to get your foot in the door to get that basic job. Otherwise, how are you supposed to sign up for an apprenticeship if you can't get a job and you can't sign up as an apprentice if you don't have a job? There is that.
Also, as you just said, there are ratios, and depending—I'm not sure of the numbers, but it depends on the trade—there are different ratios. If you're at a garage with mechanics and you can only have one apprentice per technician, that gets pretty expensive if you have to have a licensed technician for every apprentice. That's something the employers always have to consider.