I agree that there are many things beyond our scientific knowledge. However, this is in a large part why I don't accept it as given that anything is beyond the laws of nature. Just because we can't see how it fits doesn't mean it doesn't, just that our understanding is incomplete (and possibly wrong).
Scientific knowledge never accounts for all that exists it will always be an incomplete system because it only moves with our own inquiries, 200 years ago science doesn't say what it does now and 100 years from now it will be the same as it grows, that's why this is so important for people to understand this and not hang their hopes on it. Science does not answer questions about God or anything other than what we study in our physical universe, that we are capable of. It has no knowledge in and of itself, it's simply a reflection of what we are happening to examine, it is just a method of study.
This is why we look at other methods of study that are capable of reaching where science cannot, this would be the arena and vast body of facts and evidences called spirituality/religion, this is the method of study that correlates with the nature of the Divine. Science constantly changes, evolves as we continue to study the natural world and so no one should be putting their life and beliefs in something like this, it's a different study and incapable of currently answering questions about any Creator and doesn't even pretend to actually. Science is a neutral study it has no ideologies or opinions so if you want to consider something beyond the laws of nature (meaning beyond our physical sense perception alone) then look at religion and spirituality as a whole, look at all the NDE's, OBE's, spiritual encounters, spiritual insights, soul travel that all point to the reality that we are leaving this body when it hits the dirt, IMO there is no doubt about it. I've seen and had many spiritual experiences and I study NDE's and spiritual based testimonies and there is no single other subject or topic that is as vast and numerous as the amount of evidence from so many sources as spirituality, it's actually stunning all the information and experiences that are available.
If you want to experience higher experiences you have to be willing to examine, and apply things and let go. Flexible but not dumb or naïve, allow yourself to be free to examine things outside your current beliefs.
I don't have any thing against science BTW, I'm only against people using it as a means to answer questions where it certainly has no means of answering. We need science, we need spirituality because we need to understand both the physical world and the higher spiritual worlds. Both are realities and no need to reject one for the other, they are compatible if we don't try to use science to disclaim things it is not capable of and vise versa.