In Warsaw, a network of support greets those crossing the Polish border

“We must prepare for a long march,” said Mr. Maroczkowski, but, he said, he was amazed to see how many people from all over Europe had gathered here and were dedicated to offering help.

Most of the people who provide assistance are volunteers, charitable workers or employees of the Expo Center. Inside there are children’s playgrounds, a medical clinic, showers, toilets, charging stations and a canteen. Donated clothes, baby strollers, wheelchairs, diapers, pet carriers and other necessities are stacked in one corner.

One area has become a temporary bus depot where people can take free buses with the screen listing destinations.

Good Samaritans from across Europe are also bringing in aid, including a Hindu charitable group in Britain that arrived on Friday with a truck full of supplies. A temple group called the Swaminarayan Mandir in northwestern England felt ready to find a way to help.

It was reached by a local business woman, Kamilia Gorniak, who was organizing donations on social media and a warehouse where supplies could be stored. Then he connected the group to the Expo Center.

Ms. Gorniak said she felt proud to be Polish when she saw the countless charities, volunteers and those offering extra rooms.

“In this dire situation, we gathered together and really, I don’t know anyone who isn’t helping,” she said.