BEIRUT—Drenched with sweat under a scorching August sunshine, Mohamad Sheif paced back again and forth on Thursday afternoon in front of the blast-ruined metal entry gate to the port of Beirut, determined to get in and look for the rubble for his missing cousin.

“I will go and dig with my bare arms to obtain him,” reported Mr. Sheif, 56 several years aged. But a squad of camouflage-clad soldiers blocked him—and others seeking for misplaced liked ones—from signing up for the formal rescuers combing the twisted wreckage within. “No one is encouraging us,” he reported.