No.
I know some kids below the age of 13 that are excited to get a job, and I agree, getting your first job is very exciting. However, I don't think anyone below 14/15 should apply for a corporate job. At that age, I think you should focus your full attention on schoolwork. Sometimes it can be hard to balance your job AND school at the same time, which could cause you to fall behind or develop an unhealthy schedule trying to find time to do the work.
There's also the concern with the fact jobs like being a waiter or cashier are very social. That means you encounter a lot of people daily, and sometimes those people aren't good people. They could potentially put you in stressful situations or do something inappropriate to you, and some kids at 12 are too naive to recognize the signs before it's too late.
Lastly, kids mess up. Like, a lot. Imagine you want to get a quick coffee before you need to get school/work, and the 12 year old serving you messes up your order twice, making you late. Hiring kids would just be a plain inconvenience to employers at that point.
I think job training should be available as an extracurricular in middle/high school, so when they are old enough to work they'll be prepared for it.