Can I use a tourist visa to find a job in Korea and then change my work visa?

It's impossible. It is illegal to find a job with a tourist visa. Doing illegal labor is illegal, without any protection, and it also violates local laws. In other words, your job is not protected by law. If your boss is in arrears with his salary, you may be reported by others and so on. If you are found to have an illegal job, you will be repatriated immediately, not to mention changing your work visa. That's impossible.