HEIDE, Germany — When Ayham Ebrahim fled the war in his native Syria in 2016 and joined his wife, a pediatrician, in Germany, he was eager to continue his career as a doctor of internal medicine.

But after arriving in the country that was offering them refuge, instead of finding a system eager to put his talents to use, Mr. Ebrahim said, he encountered hurdles and delays that left him discouraged, demoralized and frustrated.

It took months before he could even apply for refugee status. That delayed the start of his required German-language classes. Then, his wife was offered a temporary job at a research hospital here in Heide, some 50 miles west of Kiel, the capital of Schleswig-Holstein State. So he moved with her.

But no professional-level German-language classes were offered in the smaller city, so he was forced to commute two hours each way to complete the course.