SHANGHAI—On her weekend off, saleswoman Liu Jiahui and a couple of friends rode the subway for two hours and then waded through thick crowds to experience China’s newest theme park: Shanghai Disneyland—some six weeks before it officially opens.

Disneyland’s periphery is drawing thousands of people daily, as anticipation builds for the park’s long awaited opening in mid-June. Some, like Ms. Liu, rode the subway to a newly opened jumbo-size station with colorful silhouettes of Mickey Mouse on its escalators. On a multilane boulevard...