You could get it now. You just need a very powerful telescope that you send to somewhere a billion light years away faster than the speed of light, and take pictures along the way.
There is a thin slice of space in which photons are bent 180 degrees around a black hole.
Given sufficient resolving capability, you could theoretically zoom into that slice and see earth as it was 2x the distance in light years ago. Realistically it would be a dusty noisy mess, but there are photons coming back to earth after bouncing off in the direction of the center of our galaxy 50,000 years ago.
Actually, even more than that! There is a very narrow region where photons can actually orbit a black hole multiple times before escaping. In fact there is a region where photons may orbit indefinitely!
The article mentions the photon sphere, but is there any source on "orbit multiple times before escaping"? My experience is just in Kerbal Space Program, which is a 2-body approximation, but afaik once you are in orbit, you can't escape without changing your velocity. Also, 180 degrees is the exclusive limit of a gravity bend; less than 180 is not an orbit, but as soon as you reach 180 degree bend, it becomes an orbit.
Of course, with 3-body things get much more complicated. For a third body to pull photons out of a photo sphere, fascinating and I can imagine it happening, but I haven't seen any sources along these lines.
With all of the mass inflow there is likely a very turbulent gravitational environment just outside of the event horizon. This could be sufficent to provide a little transient local lensing to kick a photon back out (or in).
Not so bad. Assuming a spherical Earth in a vacuum and a bunch of other slightly less reasonable assumptions we have:
1E+45 photons from sun per second
1.49598E+11 distance to sun in meters
6365000 earth radius in meters
2.81229E+23 surface area of solar flux at earth orbit
1.27276E+14 surface area of earth exposed to sun
4.5257E-10 ration earth area to solar flux
4.5257E+35 photons hitting earth per second
6.49E+15 one light year in meters
1.947E+25 meters in 3 billion light years
4.76367E+51 surface are of sphere 3 billion ly across
9.50046E-17 photons per m^2 at 3B ly
1.05258E+16 m^2 per photon
57883255.23 radius in meters for mirror to reflect 1 photon/second
57883.25523 radus in km (Only 10x larger than Earth!)
Then given a reasonably competent engineer to make a descent mirror with no aberration and a good telescope on a clear night away from the city, and a good bit a patience, you could watch a replay of the last 3 billion years.
You forgot to figure out how to communicate with said aliens faster than the speed of light so they have time to set this all up before the light, which has a 3 billion light-year head start, gets there.
