The Biden administration has started allowing some migrant families seeking asylum to enter the U.S. at legal border crossings for the first time since the pandemic began more than a year ago, according to people familiar with the process and government data reviewed by The Wall Street Journal. In the first three weeks of April, about 880 people traveling as families have been processed at border crossings and allowed to enter the U.S., according to internal Customs and Border Protection data reviewed by the Journal. Though the Biden administration has said the border remains closed to nonessential travel and asylum seekers, it has been making exceptions for some families and unaccompanied children, government officials confirmed Friday.