BEIJING—As the U.S. and China gear up to slap each other with tariffs Friday, Beijing’s leadership faced the thorny question of whether to strike first, or let Washington take the lead.

In response to the Trump administration’s plan to impose tariffs on $34 billion of Chinese products starting 12:01 a.m. Eastern time Friday, China pledged to retaliate with levies of the same value at the same time. But since Beijing is 12 time zones ahead of Washington, that meant China planned to put its tariffs into effect at 12:01 a.m....