Installing ceiling fan. House built in 1944. The wires from the ceiling are green and white. No black wire. The old fan I took down looks like the blue and black fan wires were connected to the white wire. I have included a photo of what I’m seeing. Perhaps someone could help.
I think you have to resign yourself to removing some more ceiling drywall material.
You must find out where that white wire goes, why it's not in a cable or conduit, and why there's no black wire. You also want to make sure that the bracket installation is strong enough to hold a ceiling fan, and correctly install the proper fan-rated junction box.
You're not going to do that through the tiny hole you now have.
Start with that obvious patch material toward the top of your picture. I think you'll find that replacing a 16" x 16" section of ceiling is not really any harder than replacing a 5" x 5" section.