A laser would work better. Over vast distances, a giant mirror would eventually scatter the light, not to mention would be super inaccurate.
Speaking of inaccurate, even if we could shine a mirror or a laser, it could be millions of years until that light reaches any other civilization, then they would have to travel millions of lightyears to reach the point of origin of the “smoke signal”.
I say “point of origin” and not “Earth”, because our galaxy would have also travelled far from the spot we were in when we fired our laser. The Milky Way travels at over 2 million km/h, so even in a measly million years, that puts us over 2 trillion km from where we started.
You can probably see where this is going.
I’m of the mind that we are undoubtedly not alone in the universe - the sheer scale and endlessness of it tells us that there are an infinite number of possibilities. There most likely are other worlds that formed and evolved in the exact same manner as ours, maybe even under conditions so perfect as to cause them to follow the exact same path as us.
Though the unfortunate truth is, we probably will never encounter another species. There could be an infinite number of ourselves, but we are forever separated by the ever expanding breadth of space and time.