PARIS—Iga Swiatek became the women’s tennis world No. 1 quite by accident this spring. She was playing a tournament in Miami when some shocking news blew up her phone. Out of nowhere, the top-ranked player in the world, Ashleigh Barty, was retiring at age 26.

Swiatek’s first reaction was to cry. Her next move was to figure how she could hold onto that No. 1 spot for as long as possible.