The answer to this question is unknown. People speculate that it could happen, and a major theory suggests this may be how life on earth began. It is called Panspermia and you can read about it on Wikipedia

However there has never been any undisputed scientific evidence that this is true. The idea is mostly science fiction at this point. A young person such as yourself could go on to study and do research in this area and maybe you will be the first person to discover evidence that life came to earth via "space dust".