Yes, even though airline personnel sometimes refer to KIX as "flying into Osaka," the airport is actually quite a way to the south of the city proper.

However, if you stay in the Namba area of Osaka, an express train leaves from Nankai Namba at 5:30AM and arrives at KIX at 6:17AM.

If that timing works for you, you can take your pick of hotels in all price ranges in the Namba area.