A cool achievement would be, observe the moon/earth separation event(s)
A cool achievement would be, observe the moon/earth separation event(s)
The bigger problem is all the dust and other stars in the way. I’m not aware of any black holes close enough that would have a direct path for the light to cross without being absorbed and scattered.
Also, the foreground galaxy/supermassive black hole in the Cosmic Horseshoe is 5.6 billion light years away, so any light that could come from our solar system, go around the black hole, and come back to our hypothetical hypertelescope would be over 11 billion years old - almost triple the age of our sun.
Saggitarius A* in our own galaxy is, of course, directly in the elliptic and therefore badly occluded by dust, but it would be interesting to look at as it's only 27k light years away. In the absence of that pesky dust, it would give us a picture of the solar system as of the Paleolithic. Andromeda, at 2.5 million light years away, would give us 5-million-year-old light. There are other black holes in the Milky Way on the order of a thousand light years away which are not at the center of the galaxy but have masses comparable to or slightly larger than our sun, these are far closer (within a few thousand years) but have much smaller gravitational fields. Luminous intensity drops off with the square of the distance, but I'm not sure how the gravitational field strength affects the ability of a particular galaxy to bend light.
It is possible to get a deflection angle of 180 but under a few million solar masses, hitting the “sweet spot” in between the photon sphere and the boundary of the shadow would basically be a once in the lifetime of the universe type probability, if it were possible at all. At billions of solar masses that sweet spot become much bigger, but then those are much further away.
In this insanely hypothetical scenario, would it be possible to see a sun before our sun? (In the same galactic vicinity)