There are zero airlines offering flights to Osaka. The most direct route isn’t necessarily the cheapest – being flexible is key to finding the lowest airfare rates. For example, try searching by month to see the best time of the week to fly.
Osaka Itami Airport is just one of the airports in Osaka. If you're not set on a specific airport, try changing your search from Osaka Itami Airport to Osaka to see a broader range of flights – they might be cheaper.
During this peak season, accommodation prices often increase too, so it's best to book early. Or you could keep your fingers crossed and hold out for a last-minute deal.