My Grandfather Doesn't Exist

I have recently started working on a family tree. It has been fun, interesting and frustrating all at the same time. Luckily for me, an uncle on my father's side has been working on their side of my family for a few years. Even more luck for me, Sister had a copy of all his work and sent me a copy too! I have traced on branch of our family all the way back to 1485. I just keep following the bloodlines. I think one day I would like to add on all the miscellaneous cousins and their lines too. Just to see how many I can get. There is a website called Geni that will let you build your family tree for free. I am going to find a way to make this a part of our homeschool. I think Z could really benefit from the researching and knowing where his ancestors came from. I have learned that my grandfather apparently never existed! I have a copy of his birth certificate and a copy of their marriage license. They were my grandmothers hard copies. But when searching online I cannot find him anywhere. I can't find his birth, their marriage record, his death, social security, nothing. I have only initials for his parents so that isn't helping any either. I keep hoping that someone else will come across his name in their family and I will find more information that way. How do find someone when the government says they didn't exist?