Can I do it without using a UV sphere?
Could you say why you don’t want to create a hemisphere from the UV sphere? It might make it more clear what you need 
You could add a circle, delete half of it, and then use the rotate tool to extrude it 180 degrees. I’m not really sure if that is what you are looking for.
Why would you have such a bizarre requirement anyway?
you can make a sphere with Icosphere also
which is not a UVshpere!
is that what you need ?
salutations
subdivide a cube then mesh/ transform/ transform to sphere.
Sub surf a ico sphere gets a different mesh.
Scripts extra object or solids might have something you can subsurf for a different mesh