Even a nice, fat check that lands in your lap is a mountain to climb when you’re Juan Jordan.

He’s a single dad. His daughter is a chubby-cheeked cutie who just turned 1. Her name is Kai, and she keeps smiling even when she’s plopped in a stranger’s car, then made to wait in an office while the stranger holds her and she cranes her neck to track Daddy.

But a day like that is easy given what she’s seen in her one year on this earth.

At 2 months old, Kai lived on the streets with her dad. They bedded down in bus shelters, abandoned cars and on friends’ couches.

They finally — thanks to help from the Washington Legal Clinic for the Homeless — landed a spot at the old D.C. General Hospital, which is serving the city’s ever-growing population of homeless families. They’ve been waiting eight months for transitional housing.

Juan Jordan holds 1-year-old Kai. (Petula Dvorak/THE WASHINGTON POST)

The shelter is safer, certainly. But Jordan, 45, is forever questioned, challenged and probed because it’s just him and his little girl.

When he goes to check on the status of a child-care voucher, or a housing spot, or even at the doctor, he gets the same question: “Where’s the baby’s mama at?”

“Why don’t they ask all those mamas that every time? I don’t hear everyone always asking them: ‘Where baby daddy at?’ Nah-aw. But they ask me. Every. Single. Time,” he says, unleashing.

When he can get away with it, he rolls his one good eye at them and keeps rocking Kai or straightening her pink and pinker outfits.

For those who hold his fate in their hands — the clerk at a voucher program or a case manager — he carries around a white plastic H&M shopping bag with all her documents inside: birth certificate, health records, doctors’ bills, every prenatal visit receipt he could get from her mama.

And he’s got the paperwork from the drug rehab that Kai’s mama was sent to. And the one she was kicked out of. And the court papers for her drug charges, her mental health evaluations, her court no-shows. That’s just so he can prove that Kai’s mama isn’t really around, waiting with a diaper bag and a mother’s gentle touch.

Kai was unplanned and unexpected. The couple met at an Alcoholics Anonymous meeting and bonded over tough times rather than hopes for a bright future.

“I had my small troubles with the law. Minor stuff that was all about growing up to be a man in D.C.,” he told me. A court search didn’t show anything for Juan L. Jordan. He said the last time he was in trouble it had to do with his drinking and it was in 1993.

The court records I searched, based on the mama’s name from all those documents, backed up everything he said.

I met Jordan in December, when I was interviewing folks on whether they had any regrets about having kids.

Jordan didn’t really want to talk to me, but he obliged. He said he wouldn’t change anything, even though he and Kai were living in a shelter.

“Nah. What else would I be doing that means anything?” he replied. “You just change your priorities. And now, she’s my priority.”

Some readers were moved by his story and sent me cards to deliver to him.

Jordan had recently been laid off after years as a building maintenance engineer. He didn’t have a working cellphone and had no permanent address — just the front desk at a shelter manned by surly guards who wand every parent, child, stroller and grocery bag with a metal detector.

Every few days, I left a note at the desk: “Mr. Jordan, please call me. I have something for you,” I wrote.

Finally, when he got his cellphone working on a good plan, he called.

We met outside. I tried to take a picture of him with the greeting cards, to send readers proof of delivery.

Jordan scowled at me and tried to move away, as a handful of onlookers leered. He’s not a particularly camera-ready man, with the one white golf-ball eye, a mean scar across his cheek and an unsmiling mouth. But that wasn’t it.

“I don’t want anyone to know my business. And if they think I got a lot of money? Lord have mercy, we won’t be safe,” he told me.

One gift was a bank check for $1,000. “Can you drive us to the bank, Ms. Petula? I’m afraid they won’t cash it for me,” he said.

I didn’t understand but opened the car door.

Hours later, after he produced his ID with no fixed address, his Social Security card, his medical records, the paperwork for Kai, the letters from readers, two tellers still wouldn’t cash it. Finally, a branch manager took him into her office, closed the door behind them and listened to his story.

An hour later, he had some cash in his pocket and had filled out the paperwork to open a savings account for Kai. This is the determination it takes to get out of that deep hole he is in.

If this is the process to simply cash a check when you’re without an anchor, imagine how hard it is to find work, housing and child care when your address is a shelter and a 1-year-old is clinging to your neck.

Each day, Jordan wakes up, gets the baby fed, cleaned and dressed, then heads out to stand in a line, produce more paperwork, find that one manager who will listen to him.

Every day, he climbs a couple small steps up that mountain.

To read Petula Dvorak’s previous columns, go to washingtonpost.com/dvorak. Follow her on Twitter @petulad.