Amina Tsoi’s twin babies are healthy girls. They squabble, as siblings do, and they both have a curious appetite for cheese, “like little mice,” their mother says. But they are small for 1-year-olds, a legacy of their premature birth during the first weeks of Russia’s invasion of Ukraine.

For seven months, Ms. Tsoi had enjoyed a happy and healthy pregnancy, largely without complications. Then one February morning last year, explosions boomed through the town where she was living, near Mykolaiv, in southern Ukraine, which faced increasing missile strikes and ground skirmishes.

“My mother-in-law entered our room and said, ‘The war has started,’” Ms. Tsoi said. “And I started to panic.”

Ms. Tsoi, then age 20, escaped any bombardment and was seemingly unharmed. But in the ensuing days, she lost the sight in one eye and gained 14 pounds because she was retaining water. After she had an emergency cesarean section, during which she lost enough blood to require two transfusions, her daughters, born six weeks premature, clung to life in incubators.