When science says "the world is 13,000,000,000 years old", they are not saying "I was there. I have a video. I KNOW". They say "based on the evidence that I have, and based on the laws of nature that I observe, the world could have been created like this.
Or maybe not. Maybe there are other scientific laws involved that we just don't know about. We don't know everything yet, and it's possible all of our theories would't work under different conditions.
Or one can add, even if you say that from the Big Bang on everything was natural, the original yesh mi-ayin, the something from nothing, must have been supernatural. If creation is supernatural, there is no reason to stop the supernatural involment by the Big Bang, why not extend it to the end of creation. It says that when Hashem created the world, it was created fully formed. Meaning, Adam was an adult. If he would come to a doctor and ask "how old am I?" the doctor would say "middle aged". Was he or not?