I have a very confident 7 year old in a state school. DH and I went to private schools and both come from families with confident, capable parents, so that background is there.
My DD has been confident from a very young age, some of that is about being naturally outgoing. She also spent a lot of time with high quality adult interactions - her nursery was great for having high staff ratios and an expectation that the staff would be down on the floor playing with the children.
No one has ‘squashed’ her confidence. For example, at nursery she would join the manager in showing prospective parents round the nursery. I was amazed that they allowed her to do that, but they did and it made her feel great.
We have high expectations of her academically and her teachers do too - there is always a next step, even if she’s done something well. But there is also praise for doing well and particularly for creating her own challenges and achieving them.
She has a strong peer group of similar children. They (and their parents) create a culture of competition and make academic success desirable, rather than stigmatise it. They also challenge her tendency to try to take the lead excessively.
She does a range of extra curricular activities which broaden her educational experiences to something more like a private school range of subjects (that’s not why she does them). Those activities range from ones that she finds easy, to ones that require perseverance and she doesn’t have a natural aptitude for, but still enjoys. One of the harder things to provide for academically capable children is opportunities to fail or the need to persevere to achieve and that can make it hard to develop resilience.
We also take her to interesting places and hopefully do fun things. We haven’t taken her abroad a lot, but we do go to new places and look for things that match her interests. We answer her questions and follow through with her interests, though I do try to get her to do some stuff independently.
I think that the most important thing is that we just assume she’s capable of pretty much anything and the world is her oyster. I think that is part of the private school attitude. So if she says ‘I want to go to Japan’, I might say that we won’t take her, but she can go as an adult, like X did. Everything is within her reach.
I would like to point out that my DD is also a lovely girl, she might sound very confident, but she is pleasant with it.