As I presume you know, with inferencing you can lock movement along a single axis at a time. Now, if you turn on hidden geometry, you can see that your sphere is divided up into a grid of horizontal circles of latitude and vertical circles of longitude like a globe of the Earth. Assuming you have constructed your sphere on axis (as you should), there will always be a meridian (a great circle of longitude) parallel to the x axis and another parallel to the y axis. Grab any point on the x meridian and move the sphere along the y axis until it snaps to alignment with the vertical axis of your assembly, thus aligning it in y. Then grab any point on the y meridian and move the sphere straight along x, once again until you can snap to the vertical axis, aligning in x. The sphere is now centered on the x and y axes. Now just move the sphere along the Blue (vertical) axis until it’s at the correct elevation, or snap the equator to some point to align in z.
In other words, you can almost always align objects along one axis at a time, and frequently this is the fastest, easiest way to go. Although it’s a bit different from your present arrangement, the following picture shows a similar three-step alignment process: