It’s pretty difficult to say, honestly.
For children, developing skill depends on a lot of factors. Only one of which is natural ability. You’ve got your obvious prodigies, who pick it up right away and are competing in adult competitions by the age of 12 (like Ernie Reyes Jr). Those are extremely rare. You’ve got children with natural inclinations toward physical activity, are naturally more flexible, and simply have better motor skills than the average child. You’ve got the kids who haven’t started developing any of those yet, so everything is a challenge and training is slow. And then you’ve got the ones who are just bad at it in the beginning.
Then, there’s interest. Children learn faster when they’re interested in learning. So, a child who struggles but loves their training will learn faster than a child who struggles and hates it. Children who naturally have better aptitude will be ahead in the start, but if they don’t develop an interest or love for what they’re doing, they’ll inevitably fall behind/grow disinterested. This disinterest can occur anywhere between a few months to a few years. You can keep pushing them based on parental approval, but that will die.
Then, there’s the amount of time they spend learning. A child who is trained by their parent or responsible adult figure and spends most of their day learning is going to be in a very different place in six months than a child who only trains for forty-five minutes (standard recreational martial arts class length) three to four days a week.
Then, we have the type of training.
In traditional martial arts like karate or taekwondo, a child training for 6 months will still be a beginner. They’ll have some of the basics on lockdown (a few stances, the double punch, the front kick, and maybe they’ll have put it all together into a form) and that’ll be about it. They (more than likely) won’t have done any sparring yet unless their instructor okays it. They won’t know a lot in six months, but they will by the time they’re thirteen/fourteen. It takes two to three months to get out of white belt.
In practical (police combat training/military combat training), someone who has been in training for six months can kick your ass. You don’t put children through that unless you’re a sadist who loves child abuse. Kids can’t handle it. Children also cannot fight adults, they don’t fight like adults, and they don’t have the same understanding of permanent consequences that adults do. They are developing human beings, so work is slow.
And yeah, puberty/developing bodies have a serious effect on a child’s/teenager’s ability to perform. You’re constantly having to re-calibrate and readjust your balance, re-learn distance, all the ancillary stuff. A child’s body is changing on the regular, so every few years they take a hit where they need to readjust themselves. So, you can have a child who has excellent technique between 4-9 and then hits the awkward years between 10 and 17. (Whatever point they stop growing.) They don’t lose their skills, but they have to relearn/get used to their new body and that takes time.
The thing with training children is that its a balancing act. One of the biggest issues in fiction when it comes to writing children is that they get treated like little adults. They’re not. Children are in a constant state of growth, development, and change. Their understanding of the world is constantly evolving. It can change drastically in just a few months.
They’re also not all the same. They learn at different speeds.
When you want to sit down at write a child character or just establish their background, you need to start with specifics. General knowledge about training children isn’t going to be helpful because there are many approaches.
First, establish what their life is like. What do they do in their day to day? What is their focus? Figure out where the training fits in, who is teaching them, how much they practice.
By establishing the character’s background before you begin your research will be incredibly helpful because it narrows the field in which you need to search. If your kid was handed off to a school to focus them on martial training, which happens to countless talented children in China, then you know to begin looking at martial arts academies in China. If your character is trained by their parent, then you can start looking at historical martial artists trained by their parents. There are many of these, especially well-documented in Eastern traditions. If your child is some kind of noble, trained a few hours a day by a fencing or other kind of combat instructor then you know to look at European swordsmanship traditions to get an idea of what that kind of training looked like.
The more you can narrow down what you want, the easier your research will be and the easier the answers you need will be to locate.
Children have been practicing and training in martial combat for sport and for combat all across the globe for centuries. It is an area of study that is fairly well documented (if uncomfortable). General knowledge will help you start, but it won’t help you much.
Figure out who your child is, what their background/circumstances are, and then research similar children in similar circumstances.
Specifics are always key.