Can the scientific method be used to prove unique historical events?
The scientific method is not used to 'prove' anything. See the detailed discussion below. The appropriate methods for supporting historical claims are the methods of historical research.
The scientific method (many people now talk about 'scientific methods' instead, since the methods of physics may be quite different from the methods of biology, for example) is not said to 'prove' anything. Philosophers of science, and careful scientists, say that scientific theories are 'supported by the evidence' and that they have not yet been 'falsified' by contrary evidence.
Scientific theories are explanations that that explain the facts observed and measured in the natural world.
Scientific methods are not the appropriate methods for establishing how likely historical events are, whether they were unique or not. The methods of history are the appropriate methods for studying the evidence that supports historical events such as wars, treaties, births and deaths and so on.
I'm only guessing, but it's possible the intention of the question is about evolution. In that case, science is not evaluating history, it is explaining the facts we observe in the living world right now.
If it is about abiogenesis - the first arising of life - then the best we can do is come up with a plausible explanation of how it could have happened... there will not be direct scientific evidence that shows how life arose that will have remained until now. Life is here, and how it is come to be complex can be studied by science. How it first came to be here is a more difficult question.