You believe god exists because the Bible says so and you believe the Bible is true because god says it is true in the Bible.
Is this correct?
Essentially yes.
BUT, keep in mind that Jesus said ...
John 12:32 And I, if I be lifted up from the earth, will draw all men unto me.
YOU are included in that verse as well.
This means that you, too, are/have experiencing the convicting power of God on your engrams.
But not all people get saved, because they "pull back" from that "pull" on them ...
Hebrews 10:39 But we are not of them who draw back unto perdition; but of them that believe to the saving of the soul.
As a person uses his freewill in this tug-of-war that's going on ... the more he uses it to draw back, the more "anesthetized" he becomes to the pull.
This is why a person won't be able to use the excuse "I never knew," at the White Throne Judgement Seat.
Furthermore, here's a list of cause-and-effect evidence of God's existence:
1. Time divided into BC and AD.
2. Organizations such as the Red Cross and Salvation Army.
3. Hospitals built by Christian organizations.
4. Beautiful Christian artwork, edifices, statuary and literature.
5. IN GOD WE TRUST on our coins and UNDER GOD in our pledge of allegiance.
6. The Ten Commandments and other literature displayed in public.
7. Christmas & Easter
8. Symbols on bumper stickers and flags.
9. Public debates in the name of Christianity.
10. Crosses and billboards erected to testify of Jesus Christ.
11. Two major nations founded on His existence.