I am curious, do you think that science will arrive at an explanation? No
Science doesn't really arrive at explanations. It describes things as they are, but it can't explain them. It can tell you with great accuracy how electricity behaves. But it can't explain it. Yes, it can tell you that electricity is electrons that have been stripped off of atoms, yadda yadda. But what is the electron. And what is the force that stripped them from the atom. There is always another question. There are only descriptions of what is being observed, but no explanations of how or why.
Your line of reasoning begs the question, "is it possible for science to prove an intelligent design?" I wouldn't say that it is impossible. However I can't propose a way to do it.
I can tell you with certainty that it is very possible for an individual to satisfy themselves as to the existence of God. I have done so, rather late in life, and after being adamantly opposed to that possibility. Many millions of people have done so.
"Faith" can be misunderstood. If you tell me that you will do something, and I have faith in you, that means that I believe you will do what you say, I trust you.
Faith in God is much the same. It doesn't mean that I just have to believe that He exists, and that that is all there is to it.
Faith in God means that I trust Him. Once I have opened myself up to a relationship with him in that matter, I am able to experience his presence in many tangible and profound ways.