A day after shrugging off challenges to his autobiography at a presidential debate, Republican candidate Ben Carson made an appearance at a Christian university in Virginia on Wednesday, where a friendly crowd cheered as he disparaged the theory of evolution and promised to roll back same-sex marriage.

“People say, ‘How can you be a scientist and believe that God created the Earth?’” Carson told thousands of students and visitors at Liberty University in Lynchburg.

“I don’t criticize them. I say, ‘Can you tell me how something came from nothing?’ And of course they can’t ... And now you’re going to tell me there’s a big bang, and it comes into perfect order? ... And they say, ‘Well, yeah.’ And I say, ‘But don’t you also believe in entropy, that things move toward a state of disorganization?’

“And they say, ‘We don’t understand everything.’ And I’m not sure they understand anything! ... Everybody believe what you want to believe.”

Carson, the frontrunner to win the Republican presidential nomination in some polls, was on a four-state campaign swing following the debate on Wednesday night in Milwaukee, Wisconsin, where he claimed a minimum of speaking time but won warm applause for jokes about the scrutiny his life story has come under in the past week. Media reports have cast doubt on stories Carson has told of being offered a scholarship to West Point military academy, winning an honesty award at Yale University and other stories.

Carson told bits of his life story to thousands of students who turned out to hear him speak on Wednesday, intermingling anecdotes with a description of policy priorities for the next president.

One such priority, he said, was protecting the “religious freedom” of people who believe on religious grounds that marriage is “between one man and one woman”. Carson promised, if elected president, to push Congress to make this a matter of national law.

“We’re going to have to have a president who’s willing to work with the legislature to put things back in order,” he said, to cheers and applause.

Liberty University was founded by Jerry Falwell, the Christian evangelist, in the 1970s and has grown into a center of political activity for candidates courting so-called values voters. Ted Cruz, the Texas senator, launched his presidential campaign at the campus earlier this year.

“Have you ever noticed there’s an American way, an American dream?” asked Carson, a retired and decorated brain surgeon.

“There’s no French dream. There’s no Canadian dream. This is the most exceptional nation in the history of the world.”

Carson said he had leaned on scripture to weather tempests on the campaign trail. “I cling to it now,” he said, “when so many in the media want to bring me down because I represent something they can’t stand.”