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.
