I started over-fences when I was about a year into taking lessons. It was the barn's policy, and something they made known upfront, that students could not start jumping lessons until they'd been taking flat lessons for at least a year. . .and, IMO, that was a great policy to have.
It makes me a little afraid for the students of trainers who rush them into jumping. Or, when the trainer knows the student really isn't ready to jump but "gives in" so that the student won't just go on to another trainer/lesson barn. There are plenty of ways to develop riding ability in flat lessons while still keeping it interesting and challenging.
When I used to teach riding at a summer camp, where the girls often came in with zero riding experience, there were some parents who honestly expected their precious young 'un to be jumping by the end of the two or four-week session. A few of them even went out and bought their child "show clothes" to wear to all of the riding lessons. So, when I said "Ummm. . .your daughter is terrified of being on a horse and has zero control in the saddle. . .no jumping for a while" they were less than thrilled.