Imagine there is a supernova a hundred years ago. Lots of people see it but nobody has a decent telescope. A hundred years later we point a powerful telescope in the opposite direction, and find a huge alien mirror a hundred light years away, that allows us to watch the supernova.
Light travels at a fixed speed so a hundred years later when we build our telescope we would see nothing in the opposite direction, because the light reflected from your alien mirror would only have reached that mirror, and has another hundred years to reach our telescope.
My question is, what is the limit of such a technique ?
It's a thought experiment, not a technique.
Could we see right back to the big bang if the mirror was large enough and far enough away?
Light takes time to reach us, so when we look at very distant objects they're already telling us about the distant past. This is how we have built up an understanding of what happened in the distant past.
You might want to explore the subject of the Cosmic Microwave Background here.
In principle it would be easier to detect any radiation from the big bang directly (without a mirror) in a similar way. But the universe is not a quiet place and radiation from the big bang has literally been through everything and won't be as easily detected (if it's possible at all). We don't even have a proper theory to know what to expect to be able to detect, if anything.
All the mirror does is complicate things.