Avoid school holidays, be open minded about routing (the cheapest direct flights are twice the price of the cheapest indirect flights), pounce on a good deal as soon as you see it. Saying that, if you are prepared for some inconvenience it is occasionally possible to get deals when the kids break up from school (for instance I got Easter flights to Nagoya from Stockholm, neither ARN nor NGO are at all convenient for us but we’re making them work and saving hundreds of Euros)

There are plenty of flights to KIX (Osaka) from AMS between November 2024 and March 2025 in the €520-€600 range. Absolute cheapest flights I’ve seen are €400 return but they depart from Budapest, Hungary. €500-€600 is about as good as it gets for a complete return trip from AMS. As mentioned already, you’ll find them on Google flights.