First, it has been said time and time again here, and I will say it one
more time:  Science does PROVE anything!  Not in the sense of a mathematical
proof as you seem to want.  It is not a failing of science that it doesn't
prove things in a mathematical sense.

So what does science do then?  The scientist forms a hypothesis (or theory,
I you prefer).  Then he says "IF the hypothesis were true, what would I
expect to see in nature?"  These are the predictions of the theory.  If the
theory makes no predictions; it is useless; it is logically equivalent to
a catalog of the data that went into its making.

Then the scientist actually looks at nature (performs an experiment).  If
nature doesn't look the way the hypothesis said it should, then the
hypothesis is flawed, and it may need to be modified or discarded.  If the
results of the experiment turn out as the theory predicted, then the theory
has earned a point in its favor.  All a theory ever really does is to
gain (or lose) favor, and it gains favor with scientists by making 
USEFUL and CORRECT predictions.

This then is the vaunted "scientific method".  It is the ONLY criterion
scientists use for evaluating theories.  Evolution and most theories of 
evolutionary mechanisms pass the tests of making useful and correct
predictions with flying colors.

We provisionally accepted evolution, find data, the data was predicted and
conforms to evolutionary theory, then we continue to accept evolution
but less provisionally than before.