Khalid’s father, Abdelwahhid Ibo, 40, a laborer, and his sister Salha, 47, a janitor at a bank, said they worried about the children’s safety — but their own earnings could not feed the family.

They are among the lucky few to pass several stages of a lengthy process to win resettlement in the West.

They fantasize about Australia, but they have little choice: In a standardized process run by international aid agencies, where they end up depends on which country, if any, volunteers to take them.

But down the coast, near the Sobhi Saleh school, the Hamdi family is not so fortunate.

They rent a drafty cinder-block room beside a garbage-strewn beach. Once a fancier district called the Riviera, the neighborhood grew crowded in the 1970s with Lebanese displaced by war. Some have since emigrated to Germany and rent their ramshackle houses to Syrian refugees.

Ibrahim Hamdi, 55, worked for decades in Lebanon, returning to Syria every few months to see his family. That tradition — along with shared language and history — has helped many Syrians find their way here. But as more arrive, helping them gets harder.

United Nations cuts have ended refugee benefits for Mr. Hamdi and his older sons. And newly restrictive Lebanese policies mean that his wife and younger children, who arrived more recently, cannot register for refugee status — meaning that unlike the Jassems, they have no path to resettlement.

Mr. Hamdi has forbidden his sons from trying their luck in the smugglers’ boats. Instead, the older children look for work and plan to invest everything in school for the youngest: Ahmed, 5, is not yet too far behind the Lebanese in English.

“The crisis might not be solved for 20 years,” Mr. Hamdi said. “Both Lebanon and we are bearing the burden.”