God does not need to prove how he made the earth just like He does not need to prove that He exists. He is all-powerful and all-knowing and exists outside the dimension of time. He merely needs to speak something into existence and it will be.
The early church fathers did not believe in an "old earth" (long period for creation). Clergymen (and scientists) did not begin to seriously doubt the young earth (literal) account of creation in the bible until the nineteenth century. Partly for this reason some early church fathers (theologians) thought the earth was created instantly and the seven-day account in Genesis was an allegory. Seriously, all God had to do was snap his fingers and everything could have been done instantly. I think that is what AV calls ex nihilo.
It is hard for a new Christian to accept the supernatural after being brain washed in secular society with an antibiblical worldview. It almost drove me crazy getting my head around what and who God is after I first became a Christian. The best and maybe the only way for most people to "get it" is to dedicate their life to God (Jesus), study His word and follow Him with all their heart and He will prove himself.
Believing the Bible first and then studying it to understand who God is, and how He has a plan for me, is not an unreasonable step to find ultimate Truth (God/Jesus). If I receive a letter from someone and I want to determine the contents/claims in the letter to be true the best thing to do is question the sender and test the sender to see if it is true. I don't mean I should use doubt as a starting point but give the sender the benefit of the doubt. Scripture says to "ask and it shall be given, seek and ye shall find, knock and the door will be opened" Matthew 7:7. The Bible has Gods name all over it in terms of how he revealed himself to the authors.
There is plenty of evidence to confirm the physical state of the earth being a product of young earth creation (6,000 years) but I am not getting into this now. The fact remains that until someone gets the right worldview and has their understanding opened they will not believe. People believe what they want to believe based on their worldview. Just as the atheists call Christians blind to their (our) Bible-only view, they are blinded by their naturalism.
I like the scripture Matthew 11:28-30 which says (words of Jesus), "Come unto me, all ye that labour and are heavy laden, and I will give you rest. Take my yoke upon you, and LEARN OF ME; for I am meek and lowly in heart: and ye shall find rest unto your souls. For my yoke is easy, and my burden is light." KJV