It is the job of the plaintiff to present evidence that would influence the Court in their direction. That is not the job of the defendant.
If a Certificate of Naturalization was ever issued to Senator Cruz, that fact could be easily uncovered via a Freedom of Information Act request.
That's false.
Record Requests Frequently Asked Questions | USCIS
If the immigrant was born less than 100 years ago, you will also need to provide proof of his/her death. ...
North American Law Center
Unfortunately, there is no evidence to suggest that the parent or parents of Ted Cruz ever filed a CRBA form with the U.S. Government in or around 1970, which is why Ted Cruz released a copy of his Canadian citizenship records and not any U.S. citizenship records. At present, all FOIA (Freedom of Information Act) requests filed in search of any U.S. citizenship documents to confirm the true official U.S. citizenship status of Ted Cruz have been denied access.
Looks like someone already tried.