Little did the Afghan family know, their asylum plea was already a lost cause.
Under amendments passed in 2018, Hungary has been automatically rejecting applications of those who have passed through a "safe transit country", in this case Serbia, in what rights groups say has turned the asylum process into a cruel charade.
"They did not ask what problems brought us there, they only asked us how we had come," the 36-year-old mother, trembling with tears, said from the migrant camp in Serbia where her family is regrouping.
After their long wait, their experience of Hungary was bleak and brief.
They were shut into a transit camp made of blue shipping containers and surrounded by a razor-wire fence, just next to the border barrier.
Four months later, their application was rejected and they were kicked back to Serbia in the middle of the night.
"They brought us to the other side of the fence and left us in the forest," Asurma said.
During the 2015 migrant crisis, the border etched across northern Serbia's fertile flatlands became a vital crossing point into the European Union for migrants from the Middle East, Asia and Africa.
But Hungary slowed their march by building the 175-kilometre (110-mile) border fence four years ago, fortifying the EU's edge.
Since then, Budapest has continued to pass laws hostile to migrants, alarming EU officials who have struggled to rein in right-wing Prime Minister Viktor Orban and his anti-immigration crusade.
The "safe transit country" idea is a "novel concept that has been introduced by Hungarian officials" over the last year, said John Young from the UNHCR mission in Serbia.
"It's not the way an asylum system is supposed to work," he said.
'Causes unacceptable suffering'
The number of migrants allowed to enter Hungary from Serbia has also been systematically reduced to a trickle, from 20 people a day down to the current quota of around two families per week.
One official at a Serbian migrant camp described it as a form of "psychological torture" for those like Asurma who spend years waiting on a list.
Hungary's two "transit zone" camps have also been roundly criticised by rights groups as inhumane.
"Detaining people, including children, indefinitely behind barbed wires and fences in shipping containers is not simply unlawful but causes unacceptable suffering to asylum seekers," said the Hungarian Helsinki Committee rights group.
A new battle has been brewing since migrants reported being refused food while being forced to choose between returning to Serbia or deportation to their home country.
The Hungarian Helsinki Committee has documented 15 cases of food deprivation affecting nearly 30 people since August 2018.
Asurma, who was pregnant at the time, says her husband was also denied food for three days after their application was rejected.
In July the European Commission warned that detention conditions in Hungarian transit zones, in particular the withholding of food, violated the bloc's rights legislation.
On October 10, Brussels gave Budapest one month to respond, threatening to refer the case to the European Court of Justice.
When asked to comment by AFP, the government's press office said that all asylum seekers are provided for, but if their bid is "refused, he or she must leave the transit zone".
Although the European Court of Human Rights ruled in early October that Hungary must allow journalists into the transit camps, AFP reporters were refused entry at the scene several weeks later and have also had an official request denied on grounds of "privacy rights and keeping the peace" of those detained.
'I feel like I am 200'
After years of pinning their hopes on Hungary, Asurma and her family are now joining many other migrants in swerving westwards towards Croatia, carving a new route through the Balkans.
That path usually involves crossing mountains in Bosnia, a country with a shortage of migrant facilities, leaving many to sleep rough or in tent cities with deplorable sanitary conditions.
The next hurdle is circumventing Croatian border police, who are regularly accused of violent pushbacks.
Many migrants have reported beatings and thefts at their hands, though Zagreb denies all accusations.
In their latest attempt to leave Serbia, Asurma and her younger children were stopped by Croatian police, while her oldest daughter and husband managed to slip through.
They made it to Germany, where they are waiting for word on a new asylum application.
Asurma, however, remains in Serbia, trying to plot her next move with two teenagers and a newborn baby who has Down Syndrome and needs treatment for troubled breathing, which comes out in choked gasps.
After years of a life put on hold, her spirit is weakened.
"It is like my body has been torn into pieces from sadness and misery. Yes I am 36 years old, but I feel like I am 200," she said.