Wilde was born in New York City. Her mother, Leslie Cockburn (née Redlich), is a 60 Minutes producer and journalist. Her father, Andrew Cockburn, who was born in London, England, and raised in Ireland, is a journalist, as are her uncles Alexander Cockburn and Patrick Cockburn. Her older sister, Chloe Cockburn, is a civil rights attorney in New York; her late aunt, Sarah Caudwell, was a writer, and her paternal grandfather, Claud Cockburn, was a novelist and journalist.