Hungary’s Budapest-Keleti railway station became a temporary camp for refugees.
Yuri Kozyrev—NOOR for TIME

Over the past year, the 10-man crew of the Commander Kazakos has patrolled the front lines of the largest mass migration into Europe since World War II. At first the job offered little excitement: on a typical night this spring one or two boatfuls of migrants, mostly fleeing the civil war in Syria, would need to be rescued from the flimsy rubber crafts they use to reach the Greek islands from the western coast of Turkey. But by the end of August, the coast guard had become overwhelmed. “One night I looked at the radar and saw eight of their boats coming toward us in a line,” recalls border guard Dimitrios Argyropoulos. “I thought to myself, This can’t be happening.”

Yet it is happening almost every day. More than a quarter-million migrants have reached the Greek islands by boat so far this year on their way to claim asylum in Western Europe. In Germany, their destination of choice, the government expects to receive more than 800,000 requests for asylum this year, quadruple the number registered in 2014. And according to Greek officials, some 300,000 other migrants are waiting in the coastal towns of Turkey to make the dangerous trip across these wine-dark seas, having already paid smugglers more than $1,000 for each ticket onto one of their overcrowded boats.

The sheer scale of the exodus from Syria has left Europe with no coherent response. During a press conference held in Berlin on Aug. 31, German Chancellor Angela Merkel said the European Union must share the responsibility for taking in the refugees. If the E.U. responds to the crisis by closing its borders to asylum seekers, she added, “it won’t be the Europe we wished for.”

But Merkel’s stance is not shared across the whole of the E.U. Hungary’s southern border has become a flash point for asylum seekers trying to walk into the E.U. from neighboring Serbia, and the right-wing Hungarian government has responded by building a barbed-wire fence along the frontier and seeking to prosecute migrants who cross illegally. Yet after thousands of migrants trapped in Hungary began protesting at the start of September, demanding the right to board trains bound for Western Europe, Hungarian officials decided on Sept. 4 to charter dozens of buses to move them to the border with Austria, whose government allowed them in to apply for asylum or travel onward to Germany.

This effectively removed the last major choke point along the river of migration through Europe, which now runs practically unimpeded for more than a thousand miles from Turkey to Greece, Macedonia, Serbia, Hungary, Austria and onward to the most prosperous countries of northern and western Europe. At each of these borders, most asylum seekers now wait just a few days before they are registered and allowed to move on.

That means the typical journey for a migrant–starting from a refugee camp near Turkey’s border with Syria and ending at a reception center in Germany–can take as little as a week, making it all the more tempting for asylum seekers to set out now, before Europe reconsiders its open-door policy. The result of this shift has been clear on the waters of the Aegean, where each day thousands of new migrants have tried since the end of August to reach the Greek islands on their way to Europe.

On the island of Lesbos, most of them come ashore on the northern beaches, where miles of coastline are littered with piles of their discarded life vests and the deflated husks of their boats. Private resorts full of well-heeled European tourists often see the migrant vessels coming ashore, their passengers rejoicing in Arabic as they feel dry land beneath their feet. From there, the migrants set out on foot toward the main port of Lesbos, a journey of about 40 miles (64 km) in the blazing heat.

In the areas surrounding that port, police have set up two large camps to house the asylum seekers while authorities register their arrival. They are squalid places. The nets and tarps that provide weak protection from the sun are used to form the walls of makeshift mosques. When vans arrive with rice and bread, the crush of people sometimes erupts into brawling, and minor riots have become the norm on Lesbos whenever ships arrive to take migrants to the mainland. As of Sept. 8, there were 25,000 of them waiting to be ferried off the island, double the number registered just a few days earlier. And every night thousands more keep arriving.

“We can’t possibly handle them all,” says Petty Officer Papas of the Greek coast guard. Apart from the Commander Kazakos, there is only one ship that patrols for migrants along Greece’s maritime border with Turkey, and neither has orders to stop their little rubber boats. The coast guard’s mission is humanitarian: bring the migrants aboard and carry them to the island of Leros, about 150 miles (242 km) south of Lesbos, where authorities can register their arrival in the European Union before allowing them to travel on from Greece.

On the night of Sept. 6, when the Commander Kazakos pulled alongside the first migrant boat of its patrol, the crewmen shouted to the people inside that they had entered Greek waters, and the migrants responded with cries of joy and gratitude. They turned out to be Syrians, mostly from around Damascus, whose suburbs have been besieged in recent weeks by the terrorist group ISIS. “It is like hell there now,” said Said Abbas, a 20-year-old medical student from the Syrian capital, after he climbed aboard the Greek coast-guard ship that night.

Abbas’ uncle has already settled in Germany, and assuming Abbas makes it there as well, he plans to invite other family members to follow him. Such is the momentum of Europe’s migrant crisis that one refugee who completes the journey often pulls the rest of his family along. “We heard the doors are open. And there is no life back in Syria now,” says Abbas, crouching in the bow of the coast-guard ship beside another migrant with a newborn child in her arms.

By 2 in the morning, the Commander Kazakos had brought this first haul of migrants to the island of Farmakonisi, whose pier was the first scrap of European soil they touched along their westward journey. “Catch your breath,” Petty Officer Papas told me that night. “Now we go and get the next one.” It had already appeared on the radar, an inflatable dinghy plowing through the darkness with 43 people on board.

This appears in the September 21, 2015 issue of TIME.

Contact us at editors@time.com.

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