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.
That's some strange logic. How do you figure? Do you have a link to a scripture which verifies this? Or, is it something you've either heard, or concluded on your own?
If you don't believe in the Bible, then you don't believe in The God as taught by the Catholic Church.
The Catholic Church adds just as much leaven into their teaching/beliefs as other Christian and Jewish religions. You don't need to be affiliated with either to believe in God, the Son, or the Holy Spirit. Everything you need is in the unleavened Word of God. IMO, the leavened teachings of organized religions often confuse the truth of God's word.
You do touch on something in your statement, whether you realized it or not:
"- believe in the Bible -".
But these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.
Isaiah 46:10 "I make known the end from the beginning, from ancient times, what is still to come."
We've seen this fulfilled throughout the ages, and we're seeing it being fulfilled today. One must logically conclude God is real. Only a Divine being can make known our future.
There is much more most don't know about. Including prophecies fulfilled exactly, in timing and detail, that's almost impossible to believe. And as you delve into these, learning more about them, it becomes very obvious a Divine hand is as work.