Ed Brookover, one of Mr. Carson’s top strategists, vowed “a growing, visible effort” to appeal to blacks in states with primaries open to all registered voters. But asked specific questions about South Carolina, a crucial early primary state, Mr. Brookover acknowledged that the campaign had not begun homing in on its targets.

“Our audience there may be African-Americans who have not been participating in Democratic politics,” he said. “But that’s speculation. We don’t have data on that yet.”

Mr. Carson does have a black woman, Marnie Robinson, working part-time on outreach to religious groups in South Carolina (she played the same role for Mr. Obama in 2008). But it is unclear how much she is engaging with the black church community. Eric Davis, the pastor of a nondenominational church in Columbia with 5,000 members, said he had not even known Ms. Robinson was working for Mr. Carson. As for the candidate himself, Mr. Davis said his congregants were “watching to see if this is really real.”

And while the campaign planned to broadcast the radio ad in some states that do not plan to vote until March 15, it did not indicate whether it would air it in South Carolina, where the Republican primary is nearly a month earlier. Even the ad illustrates the campaign’s somewhat rudimentary nature: There is no mention of a website, let alone a social media address, where those interested in Mr. Carson can learn more about him or sign up to help.