On Thursday, New York City began its first day of school as it grappled with an influx of migrants. Some buildings turned away children as 21,000 asylum seekers flooded already packed classrooms.

Teachers were frustrated when they heard that Newcomers High School, a school within the same building, was already at capacity. They complained to the police and pushed students from Gotham, another school in the building to the facility across the street.

A teacher told The Post that it was a problem of capacity. They should have figured this out two weeks ago!

The migrant students proudly wore their Queens Shelter IDs around the necks of many.

Jose Gonzalez, 15, a Venezuelan immigrant, was among the students who were giddy with excitement. He said that he was not nervous about starting school in New York.

“This is amazing! I have been living in Queens shelter for the past few months, and this is what I’ve waited for. I’m happy to see everyone. “This is going to be fantastic!” he told Fernanda Beccera (19), a Bolivian immigrant.

Amir Farouk told The Post that Fatima Ayou (45), a 12th grade science teacher who is fluent in Arabic, was eager to help the migrants.

She’s glad to do this important job for the kids, the community. I’m proud of her. Farouk said that she was excited and knew it was going to be an exciting day.

Many people seemed to be optimistic despite the chaos of the scene — students lining up around the corner, and others using Google Translate on their phones to communicate.

Paola Jose, a 40-year-old Angolan father who speaks Portuguese said that his son Ricardo would do better because he knew some Spanish.

“My wife Yolanda was worried.” “I told her that he had his ID, and was prepared,” he said. “I’m glad he’s going to school.” “This is a great blessing.”

He continued, “He could understand better than me because he spoke a bit of Spanish.” I do not speak Spanish. “I told him to get on the line with everyone else.”

The migrants who came from the shelters were told that they would receive all the school supplies needed, including pens and notebooks, as well as books, backpacks and textbooks.

Luciana Becerra (14), the youngest of Donald and Sonia Becerra’s asylum seekers in Bolivia, was enrolled at school by their parents.

Fernanda, their 19-year-old daughter, translated and told The Post: “The school provided us with all the supplies. The backpack, the notebooks and the pens. “They will give her all the books she needs and the packets when she enters.”

Many parents were hopeful that their child would be able to cope with the crowds on Day 1, but others expressed frustration at the lack of preparation by the DOE.

Rosa Rodriguez, 38, a Manhattan waitress who lives in Astoria but works in Manhattan as a waitress said: “Why don’t they come in earlier? The teachers can show them the way and help them with all this paperwork and IDs.”

Alex Gonzalez, a 14-year-old boy, felt overwhelmed as he prepared for his first year of school.

“I wanted early entry because I am new.” Are all these guys going to get lost, and me? They should have allowed them to come earlier. This is my worst nightmare. I hate crowds. “I’m going to go crazy!”

George Kara Lekas from Astoria was scheduled to begin at Gotham on a Thursday, but was told to wait until the principal ushered him and his class across the street, as the building was overrun by migrant students.

They gave us a bunch of crap! No information! I am getting a late finish and I left early. Two subway stops are between me and my destination. Look at this! “I’m going try to transfer into the Academy of American Studies as soon as possible!”

Looking at the long line of students from other countries, he said, “Yes, this is why!”

There was also a chaotic scene outside PS 143, Queens. Thousands of students rushed towards the building with brown paper bags stuffed full of notebooks, crayons and rolls of paper towel.

As parents dropped off their children, some of them were crying.

Teachers helped kids enter the building by pointing to balloons – one for first grade, two or three for second and third grades.

Maria, a parent from Ecuador told The Post she could only afford to buy pencils and a notebook for her son from the list of supplies she received “because I did not have enough money.”

This is his first day. He is 10 years old. She said, “He is in fifth grade.”

The DOE provided teachers with a basic guide to help them deal with the influx.

The letter warned educators that they were on their own to purchase additional supplies and overcome any language barriers between them and their students.

Two-page instruction booklets were handed out just one day before teachers welcomed 21,000 migrants into their classrooms. This is about 2,500 students more than the officials had predicted last week.

The letter warns that school administrators should not “turn away any student” because the DOE does not track immigration status.

If there are still problems, the DOE will only offer red tape. It will tell schools that have issues to “Please fill out the Central Project-Open Arms Team Support Request Form.”

The letter’s title, Project Open Arms is the name for a partnership that was formed between the DOE and the city social services agencies to provide classroom assistance for the newly migrant student population.

The DOE hired 188 English as a Second Language teachers, and another 175 bilingual teachers over the past year. This means that there were approximately 3,400 English-as-a-New Language teachers on hand and more than 1,700 teachers speaking both English and Spanish.