What are the most effective ways to nurture intellectual curiosity and critical thinking skills in children outside of traditional classroom settings?

Start off by not killing it.

Try telling your children 50 times to be quiet when they’re being inquisitive, and see how inquisitive they are after that.

Try telling your children to stop doing something relatively harmless that will teach them 50 times, and see how adventurous they are after that.

Or don’t. Please, don’t!

Let them spend the majority of their time pursuing their interests and learning about them, and a decent-sized minority of their time doing things that don’t particularly interest them, but will serve them well in life. That’s going to look different for every child. My house is full of books, for example, and the kids are almost always building something outside, or going somewhere to do something fun and interesting, and maybe getting a few cuts and bruises along the way for good measure.