As big and as luminous as the center of our galaxy is, why is it not visible to us?
If you mean “us” as in North America and Europe that’s easy. The orientation of the plane of the eclyptic is such that the Earth’s north pole is orientated away from the center of the galaxy. We get to look out of the galaxy. So - go to Astralia and look south. You’re looking toward the center of the galaxy. It’s best to use an infrared detector on your telescope so you can see through all the dust across the 50,000 LY distance to the center.
The milk blocks the view. 