do we have any explanation how could people 2500 years ago figure out things we often find insightful even today, such as Buddhism?

Not sure what exactly needs explanation here.

How could people 2500 years ago have insights about life? I guess the same way they do today.

Why do we find those insights interesting? Probably selection bias: those insights that were too culture-dependent were already forgotten, only the more universal ones remained.

Yeah, some people had life simple enough, so they could spend their time meditating about stuff. For example those born in royal families.