Essentially, the goal is to do this:
Find a model that allows us to predict natural phenomena.
If the model can predict natural phenomena and the predictions are in agreement with the observations we can make, we say that the model is a good way to describe reality.
It is in no way the final and glorious truth. It's only a model that so far has shown to be correct.
Two sepparate models can both be correct if they both make useful predictions. In this case, the one that explains all the evidence in the simples way is considered the most complete one. Sometimes, if the other model is much more simple, it can be used for certain cases. As an example is Newtonian mechanics which is taught in school because it's "right enough" to start with, and then you can later on use it as a base for relativistic theories.
So, while you can't technically prove a model, you can show that it is practically useful by following the scientifical methods.
Just make sure that the model explains something new, or does a better job at explaining than previous models.
So a model CAN and DO make statements about things that can not be direct observed, by showing that it makes correct predictions. It is possible, and some would say inevitable as we spend more time into it, that sometime down the road, an error with the current Big Bang theory is found, which means it's revised into a completely different model. An example is the speculations regarding branes that is going on in the field of string theories, which shows a slightly different view on the start of the universe.
[This message has been edited by Melchior, 04-01-2004]