WASHINGTON—The U.S. government picked up nearly 19,000 children traveling alone across the Mexican border in March, authorities said Thursday, the largest monthly number ever recorded and a major test for President Joe Biden as he reverses many of his predecessor’s immigration tactics. A complex mix of factors in the United States and Central America drove the increase. It has coincided with the Biden administration’s decision to exempt unaccompanied children from pandemic-related powers to immediately expel most people from the country without giving them an opportunity to seek asylum. Children are instead released to “sponsors” in the United States, usually parents or close relatives, while being allowed to pursue their cases in heavily backlogged immigration courts. Authorities encountered 18,890 unaccompanied children in March, according to U.S. Customs and Border Protection, well above previous highs of 11,475 in May 2019 and 10,620 in June 2014 reported by the Border Patrol, which began …