> Yes, both civil and criminal cases can try the case to a judge, called a bench trial. Both sides have to agree to that however, since technically both sides have a right to a jury trial.

The government does not have a right to a jury trial, because the government doesn't have rights. (In the federal system, for example, government consent is required for a bench trial in the Federal Rules of Criminal Procedure, but because that is not a right, and the defendants right to a speedy and public trial, there is at least one case where a federal court, when jury trials were suspended because of the pandemic, conducted a bench trial under a defense jury trial waiver despite the government refusing consent and preferring jury trial.)