Get kids designing - creating their own design challenges and going through the design thinking process in clubs. For a cross cultural element how about using an online portal like Open Ideo Junior?
Create design clubs at schools for any ages. For the younger ones leaders could suggest challenges - for the older ones the leaders could support them to come up with their own challenges in a particular field.
The club could have challenges linked to curriculum in the school or it may be purely young person led.
These might be "how can we build something" challenges through to (for the 17& 18 year olds) huge social challenges like - How can we create political systems that will enable the changes we need to make to address our climate change challenges?