we are u.s. citizens. flying in from singapore. landing in beijing on tues @ 4:30pm

Hi, after your visit, will you go back to the US or go to a third country? If so, maybe you can take advantage of the 72-hour free transit policy, then the travel entry permit is not needed. According to the feedback of some travelers, the “72 hour” period starts from the midnight following your arrival, which means your layover time is not beyond the period. However, some travelers said they contacted the Beijing Immigration Office and were told that the period is calculated from the schedule arrival time. If so, your layover exceeds the time limit. Therefore, I think you had better apply for one tourist entry permit before your travel to make your trip guaranteed.