Well, considering the reflected light would take just as long to return, you probably wouldn't see it if it were at that point. The light reflected from us would have to reach the mirror, then reflect back, doubling the time frame of the distance you are looking at. One of those fun space-time things to contemplate but only a few in the world can calculate (I wouldn't even pretend to try..)
OK, now this is the PBR thinkin’ more than me, but wouldn’t the image in the mirror merely be of the place the scientists were standing at the moment of the big bang?