scientific method will never be able to prove the past. It can't even prove whether a person has a soul or not. It will never ever prove a big bang though millions will and do swear that it does.
The same argument is true for things more mundane than evolution. Physics: did the sun rise yesterday? Will it rise tomorrow? History, literature, art, chemistry... how can we PROVE that things existed in the past, or that the laws of the universe are constant? Well, really we can't. We can never know that the universe wasn't just created by God yesterday, with all the evidence and memories merely here to fool us into thinking it is older.
But I doubt you would accept that as a reason to stop teaching history in schools. No one alive today was AT Valley Forge, but should we stop teaching about George Washington and the Constitution? You did not see Shakespeare write his plays, or Leonardo paint his art, or Columbus sail to America, or Pastuer culture his microbes. No one alive today can personally vouch for the existence of Jesus - none of us was actually in Judea 2000 years ago, but should we reject Christianity on that basis? Of course not. We accept these aspects of our historical record based on the evidence existing today for their occurrence.
Likewise, we accept the evidence of the natural world for events far older. We know Vesuvius exploded because we see the ruins, and the Romans made records, and also because the geologic evidence supports it. And we are finding out about the flooding of the Black Sea basin 6000 years ago on the basis of geologic evidence. These observations are no different from conjecture about the authorship of Romeo and Juliet, except that the pen used was not set by humans, but by the natural processes of the world. And so the evidence for evolution: observation of the natural world and experimentation. But you would not discard all of our history from the classroom for such a silly conjecture (the idea that God is a vicious jokester who delights in deceiving humans), so why would you discard evolution for the same reason?
Because God would seem more the vicious jokester for writing the book of Genesis and describing the creation the way He did if He really made the universe over 15 billion years through evolution. There are many Christians who have submitted to pop science and believe that the universe must be old. If we see starlight from 10 billion light years away then the universe simply must be 10+ billion years old.
These people feel that God is a trickster for saying the universe is young but making it look old. They fail to consider that when God made Adam He made him an adult. Scully would swear that Adam was 25ish years old 2 seconds after God brought the dust together and made him.