"If God does not make Himself known to me, then He does not exist?"

First of all, before I go in to all of the reasons that this is not sound logic, I first want to say that God has already made himself known to you. 

How do you think you know about him in the first place? 

There are hundreds of recorded instances in the scriptures of God making Himself "known". 

Now you can reject the fact that He has already "made Himself known"-- You can reject the testimonies and histories given of every prophet from Adam to Malachi and write them all of as liars or insane. 

You can reject the witness and history given of Jesus Christ and call him a fraud and a liar a long with the multitudes who followed Him and witnessed His miracles first hand.

You can reject the witnesses given of Paul, Peter, John, Matthew, James, and Luke who traveled with Him through it all among many hundreds to thousands of others. 

You can reject the testimonies given in the Book of Mormon from Lehi down to Moroni and just categorize the Book of Mormon as a giant delusion or fraud in which starting at the age of 14 Joseph Smith had his entire family convinced that he was absolutely telling truth through it all OR starting at age 14 he suffered from numerous delusional hallucinogenic trances over a period of many years which was exceptionally intense during a period of time that lasted a few months and resulted in him writing a five hundred page historical novel with hundreds of names, extensive cultural and technical details, manners and customs, arts and industries, political and religious institutions, rites and traditions with complicated military and economic histories that covers thousands of years with no large gaps; keeping a number of interrelated local histories going on at once, including religious controversy and philosophical discussions. He managed to get none of it to ever contradict itself and wrote it all essentially without any changes beyond punctuation OR he lied and so did his entire family, including his mother and father and numerous other witnesses who gave their names as eye-witnesses to both the book and to the translation of the book—either that or his entire family were all experiencing a form of group and individual hallucinations about the same thing. You can reject the testimonies of modern prophets and Apostles from Joseph Smith all the way down to Thomas S. Monson. You can say that all of these prophets and Apostles are all delusional or liars.

If you can write all of that off, then God has not made himself known to you.

Or.

You can exercise some faith, and ask God directly and get a manifestation from the Spirit as many millions of have done and testified of.

Also-- if you have only studied the records about God from one source... can you honestly say that you have actually searched for God? If your mom asked you to look for your shoes and you looked in one room-- would she really be content to say that you had really searched?