A 33-year-old cryptocurrency investor named Denys, No. 1170, said he had paid a smuggler 5,500 euros to guide him over mountains and through dense forest to cross into Romania. “I didn’t want to fight. I don’t know how to fight,” said Denys, who declined to give his last name because he had fled in violation of Ukraine’s order barring military-age men from leaving the country.

A friend in Poland, he said, planned to put his beloved American Staffordshire Terrier on a flight to Chicago once he and his girlfriend arrived there.

Like many of those waiting at the border, he said he had never contemplated immigrating to the United States before the war. “I had a flat, a car, a dog. I was happy,” he said, standing outside the tent he was sharing with his girlfriend, Rina, and two other people. A sign in Cyrillic posted on the side said: “Don’t leave food on the ground. Keep rats out.”

The family of Daria and Sonia Speranska, two sisters, was cut off from the world when rocket fire hit a village outside Kyiv where they had sought refuge. With no power, the sisters said, they boiled water in the fireplace and rationed food. On the 10th day, they managed to escape in a convoy, and eventually, their parents convinced them that they must depart for the United States, where they had friends.

“We had no desire to leave to another country. We had a great life, we traveled,” said Daria, 24, who works in information technology.

Sonia, 16, said that she had agreed to come “only because I knew my sister couldn’t go without me; I’m the strong one.”