You can verify that his mother received free Canadian Neonatal Healthcare.
You can verify that those benefits were only given to Canadian citizens at the time.
You can also verify that while Canadian citizenship was easy to obtain, Canada did not allow dual citizenship until 1976.
You can find threads from the time of the primaries that go into great detail.
Parents of children born outside the country have to file to have them recognized. There are records of exactly how Ted Cruz was recognized as a citizen and when.
He could clear it up if he wanted.