Exhausted but smiling, a migrant father with a young child strapped to his back gathers his family for a selfie to celebrate illegally crossing over the border into the US at Eagle Pass, Texas.

Behind him, a mass of hundreds of other asylum seekers who had made it alongside them Tuesday crush behind him, next to the border’s razor-wire fencing.

The southwest border has been besieged, seeing upward of 10,000 people a day handing themselves over to officers for processing.

And there is no end in sight as the hordes keep coming, with Costa Rica declaring a state of emergency this week as thousands of migrants flood over the country’s border heading north to the US.

Here The Post offers a rare firsthand account through the eyes of a witness on the front lines of the border crisis who followed the journey of the selfie-snapping dad as he made the final push to cross the Rio Grande River to reach the US.This is his account:

I joined the mostly Venezuelan group after they had worked their way up near the border by hiding on a freight chartered through northern Mexico.

They had been battered by the wind and elements and, as the train had not stopped in many hours, had little chance to eat or drink.

As the sun set over the Rio Grande, we could see Eagle Pass, Texas, to the north. I was accompanied by a local who knows Piedras Negras, Mexico.

From the train tracks, it’s a hard 15 miles over rough terrain to the US-Mexico border for the migrants, who are all ages from elderly to toddlers. Some barely have shoes left, worn down from the hundreds of miles they have walked.

Once they got to the river, the smugglers were waiting. The migrants knew they would have to pay the cartel in order to be allowed to cross the river, as no one crosses without their permission.

Money changes hands, but the transactions are done discreetly, so it’s hard to say how much. The human traffickers were aware US journalists were documenting the crossing, but didn’t menace anyone and instead simply asked not to be photographed.

The smugglers separated everyone into groups of 50 to 100. They then staggered them, telling them exactly when to cross.

Everyone waited their turn, following the orders of the smugglers, one of whom acts as a guide, getting into the water and testing the route along the riverbed to make sure it’s crossable.

Once the migrants are in the freezing water, they are directed to hold on to a rope to help stabilize them.

Some were caught off guard as they entered the currents of rushing water and took a few uneasy steps, trying to balance.

Most people held on to the rope for dear life where they could, and others held hands — hoping to stabilize themselves better during the crossing.

Many of those in the water were families — sometimes women with children traveling alone. Most parents put their kids on their shoulders to try to keep them out of the water completely.

Even among the adults, most of them were not strong swimmers, or even used to the water.

One mom held her infant wrapped in a blanket close to her chest, with only the baby’s bald head visible near her face. One female toddler was placed inside an inflatable orange and lime green car for the crossing.

The smuggler guide went back and forth across the river multiple times, helping his cargo — especially the elderly and children — cross. The water was very rough, especially for those holding babies, and there was a lot of screaming.

We could hear the coyotes telling the migrants, “Don’t worry, this is nothing. Nothing is happening here.”

The Rio Grande’s currents are notorious for sweeping away small children — ripping them out of their parents’ arms.

In just one week in 2022, two children drowned and a third was rescued from the water.

Many migrants don’t fully understand what they’re getting themselves into.

Recently, the bodies of two migrants including a 3-year-old boy were pulled from the river north of Eagle Pass, Texas.

Even with a relatively tame current, the sheer force of the water takes a toll on the human body. The day after crossing, I’m sore in my arms and legs. It’s hard to move.

Those who crossed the river Tuesday had to wait in the water on the opposite side of the bank for at least four hours.

After that, they were finally allowed to walk up the banks and turn themselves over to the US Border Patrol, at which point I had to leave.

The huge surge of migrants has overwhelmed the US’s ability to intake and process people effectively and decide who has a legal basis to stay in the country and who should be ejected.

Border towns like Eagle Pass and El Paso have said they’re at their “breaking point.”

The latter showed over 7,000 people in Customs and Border Patrol custody on Wednesday, way over its capacity.

As conditions worsen in South America, with drug cartels moving in and economic deterioration, more people than ever are moving north.

Costa Rica’s state of emergency comes as 84,490 people entered the country from the south in August alone, according to CNN.

Another 60,000 have already traveled through this month — filling up the nation’s refugee camps.

Those who were apprehended by the Border Patrol on Tuesday will be detained while they have their asylum claims evaluated to see if they meet a threshold. Anyone who doesn’t will be deported to their home country or returned to Mexico.

Those who are allowed to remain in the US to pursue their claims further are given a court date at the destination of their choosing and released.

In most cases, it will be years before they see a judge or present their case, by which time they are likely to have settled into life in the US.