Newborns lack the capacity to petition anybody. His Cuban citizenship at birth had as much validity as his US citizenship. His US citizenship is conferred by Act of Congress, otherwise he would be an alien. He is a citizen contained in the "naturalized" part of the 14th amendment to the US constitution.
I've gone around in this circle with a few people who hold as you do, most of whom haven't read the law (US constitution and SCOTUS precedent re: citizenship to a person born abroad), and those who have read the law and maintain Cruz is not naturalized have to either engage in some form or intellectual dishonesty or magic thinking.
By law he was a citizen at birth due to his mother’s citizenship.