Is the existence of life in other galaxies that are relatively the same distance we are from the sun possible?
You speak of galaxies, but I think you mean solarsystems.
Earth is in the zone where water can be flowing, which is neccesary for life to exist. It is not too far away from the sun, and not too close.
Scientists have already found planets that are in that zone. Though we can't check the planets out, so we don't know if they actually have life.
It is quite unlikely that there isn't life on other planets in the universe.