Mayor Zohran Mamdani was joined by Gov. Kathy Hochul on Tuesday to announce a milestone in the rollout of his universal childcare program — even as big questions remain about the citywide buildout of the program.

“The goal here is to make it affordable to raise a family,” Mamdani said after meeting with one of the 2,000 families offered a spot Tuesday in phase one of the 2-K program.

The city said it received 5,700 applications, meaning there were almost three applicants for every seat.

“Today, 2,000 families are going to click on their inbox, and their lives are going to change forever,” Gov. Kathy Hochul said.

Universal childcare is one of the mayor’s signature initiatives. The 2-K program will expand from 2,000 seats to 12,000 next year, with the mayor promising a seat to every family who wants one by the end of his first term.

But the cost of full universal childcare is unclear. Mamdani has projected a $6 billion price tag, but a new report from the Center for New York City Affairs at The New School puts the figure at $8.7 billion to $9.3 billion.

“With this model, we certainly demonstrate that a lot more money is needed,” Lauren Melodia, director of economic and fiscal policy at the Center for New York City Affairs, said.

Melodia, the study’s co-author, said there are many unknown variables, including the total demand for childcare. But the report said the city needs to build in higher pay for childcare workers.

“We already know that there is [a] historic undervaluation of care work,” Melodia said. “People are not getting paid enough to work in the field. There’s a shortage of people working in the field.”

Hochul said the state will conduct its own cost analysis. But she also can’t promise any funding beyond the $1.2 billion, two-year commitment announced earlier this year.

“I can’t commit future budgets at this time,” she said. “But I can tell you right now, I’m excited about the growth of this. This is just the very beginning.”

Mamdani said that for now the focus is on the buildout.

“In a city, in a country — in a world, frankly — where it seems that prices are only ever going up, to finally being able to tell families that the price of this one thing that they cannot live without is going down, it is something that is really at the core of what government should be doing,” he said.