Many parks will have some kind of mini climbing wall and this is a great link to proper indoor climbing centres. Having a controlled, non-weather dependent environment is perfect for building enthusiasm particularly if you have a wall where you can also entice them with the promise of cake! Pick your time carefully as going at the same time as the rock-jocks can be off putting and not everyone appreciates kids being around and children pick up on that energy. I reckon I lost a year of climbing with my eldest by accidently taking her to a big wall when they were route setting and the booming sound of impact drivers put her off.
It can also be tricky to find walls that have areas appropriate for small children. Ideally you are looking for slabby routes, initially with big juggy holds. Depending on the child, you may find they want to get stuck into the big routes on the first visit or they might need some more acclimatisation. With my two, the eldest took two sessions to get to the roped climb stage, my youngest wanted to get straight on to the biggest wall she could find. Both are great. The takeaway here is not to set your own expectations of success, the only benchmark is, did they have fun, and therefore do they want to do it again?
As their abilities develop (faster than you might expect) they may be capable of cranking out pretty hard routes but lack the arm reach to get to the holds set up for adults. Some walls cater for this with specialist route setters making lines small people appropriate so it’s worth asking around. Bear in mind that children’s bodies are in the process of growing. Try to avoid anything too crimpy and don’t work them too hard as injuries could cause a lifetime of problems. Ultimately be led by the child’s interests, ‘what do you fancy having a go at’ works better at this stage than ‘we’re going to do twenty circuits before you’re allowed to move on’. I have also been known to place sweets/chocolates on holds to incentivise ascents!