Start a career as a certified dog trainer while training and showing in schutzhund is the path I would suggest. Also, helpers are always in short supply and while you won't make a paid career out of it, you'll always be welcome at a club if you can competently put on a sleeve.
It does seem like being a paid helper is the best way to make money at this hobby.
Becoming a certified pet
dog trainer -- speaking as someone who did it for a while and then quit -- is a very very different skillset. The huge majority of your work involves people skills, not actual dog training, and getting client compliance is what you'll spend most of your time trying to accomplish. Frankly, it can be super frustrating, which is why I am currently burned out. The actual dog training skills involved are relatively simple. But if you're interested in going that road, Association of Pet Dog Trainers - Dog Training Resources
is the best place to get started (and the only reputable organization certifying pet dog trainers in the U.S.). If nothing else it's worth looking into to decide if you might
want to do it.
And the pet sector is, by far, the largest market for training services. There are some 78 million dogs in the U.S., last I heard, and the best estimate I've seen is that there are maybe 50,000 of those dogs actively competing in all sports combined (although it's tough to come up with a reasonable number because so many of them are registered in multiple organizations, and sussing out which are unique vs. multi-sport competitors is something I haven't seen anyone seriously attempt). Trying to become a sport
training professional means chasing a pretty darn small market.
I don't mean to discourage you. If you want to do it, by all means, go forth and do it. But it's not going to be a cakewalk.
edit: for clarity, the 50K number I've seen is based on dogs who are registered with one of the major organizations and actively competing in at least one trial that year. So it's probably low insofar as a lot of people take classes for sports but don't enter trials, and a lot of other people do enter trials but then stop once they've finished whatever titles they set out to get. So the number of students enrolled in training is probably higher by several multiples... but that's still an awfully small market to make a living from.