1. His mother's birth certificate
2. The Consular Report of Birth Abroad linking him to his mother's citizenship.
If what he says is true, he has both.
1. His mother may not have a birth certificate. You may laugh, but it is certainly possible. For example, my wife has no birth certificate. You can't gin one of those up after the fact, despite Obama's bungled attempts at that very thing.
2. Cruz's parents may not have registered his birth at the Consulate. There is no law requiring that parents do so. It is a smart practice. It is something I did for my oldest boy, but had I not done so, he'd still be an American citizen by birth, with or without this consular document.
So, your final statement is not as as boldly true as it sounds. If what ted Cruz says is true - and I have no doubt that it is - he may have neither of the documents that you demand, and their absence proves nothing.
I think it's very likely Cruz's telling is the truth.
However, he has come under suspicion and accusation in a POTUS race on a subject a very large percentage of the public thinks is important.
He will need to produce the paper trail to remove that cloud and get on with the race.
He can ever do so post facto, the mechanisms exist.
But, it appears he does not believe it matters, or should matter and does not look like he intends to do anything about it.