WILHELMSHAVEN, Germany—In March, the German government asked energy companies to weigh a seemingly impossible engineering task. Could a new liquefied natural gas import terminal, which normally takes at least five years to build, be erected in this port town by year’s end?

At the headquarters of the company asked to build the pipeline portion, technical director Thomas Hüwener posed that question to his team. “If no, then it’s a no,” he told them.“ If yes, then we have to commit, with all the possible consequences for our company.”