The Trump administration is preparing for nearly 180,000 migrants traveling as families to cross the southern border of the U.S. by May, continuing an already record-breaking year.

According to an internal document reviewed by The Wall Street Journal, officials at U.S. Customs and Border Protection anticipate between 51,000 and 58,000 migrants traveling as families will either cross the border illegally or ask for asylum at a legal border crossing this month. The agency projects that figure will reach as many as 70,000 in...