Of course the past exists. What, I didn't just write that? Is Cutter an idiot (yes, based on several of the decisions he made, but I wanted to give you a chance to answer the question)? I'm quite satisfied the series didn't continue but disappointed in the rationalism of humanity that it carried on as long as it did.
The past does not ‘exist’, at least, as far as we know. Once something’s happened, it’s gone, you can’t go back and visit it. The anomalies proved that this theory was wrong, and that the past had a constant physical existence. If one assumes time is linear, there is only the present, the past stops existing once it’s happened, and ceased to be the present, and the future doesn’t exist until it happens, at which point it becomes the present. I personally believe that the past exists, and thus that time travel is at least theoretically possible, but nobody can conclusively prove either way with our current science.