You do not have to be a judge to be a Supreme Court justice. Technically, I don't think you even have to be a lawyer.
No one without judicial experience would be nominated, and certainly not confirmed. Especially with the politicization of today. Not having the right judicial experience would be an easy grounds to knock out a nominee.
Besides which, such a nominee, even if confirmed, would not be able to have the right kind of influence on the court.
Maybe if he had chose a different path in life, Cruz could be on the Supreme Court. But, as it stands now, he would not be a good Supreme Court Justice. He might make a good, president, senator, governor, or congressman, but not that.