Of course you can. Otherwise, what you believe would simply hinge on who filled your head first. Without regard to logic, Mohamed might be the one you praise five times a day.
Truth and logic are VERY important to the Almighty.
My people are destroyed for lack of knowledge; because you have rejected knowledge, I reject you from being a priest to me. And since you have forgotten the law of your God, I also will forget your children.
Of course you can.
Sorry, NO you can not.
If logic could be applied to God, Eve wouldn't have gotten Adam kicked out of the Garden of Eden.
If you don't believe in the Bible, then you don't believe in The God as taught by the Catholic Church.
That's your choice, but you cannot use logic and reason to prove the existence of God, otherwise it would have been done over a thousand years ago.