The short answer is that we know a little bit about what is beyond the center of the Milky Way, but a lot is still unknown.
The bands of obscuring dust in the galactic plane are only a few degrees of arch wide as seen from Earth. Thus we can see for millions and billions of light years in directions which are only a few degrees "above" or "below" the plane of the Milky Way, even in the direction of the galactic center.
A number of external galaxies have been discovered which are nearly in the plane of the Milky Way and which are heavily obscured by dust clouds.
In 1967 Paolo Maffei discovered galaxies Maffei I and Maffei II though the galactic plane by their infrared emissions.
Maffei I is a giant elliptical galaxy which is part of the IC 342/Maffei group of galaxies about ten to twenty million light years away.
Maffei 2 is a spiral galaxy thought to be a member of the IC 342/Maffei group of galaxies about 10 million light years away.
I think that Maffei 1 & 2 are about 90 degrees from the direction to the center of the galaxy.
And it is possible that other distant galaxies have been observed through the dust of the Milky Way in directions closer to the galactic center.