Inequality is bequeathed early and hardened fast. Research indicates that by the time low-income children are 5 years old, they typically hear 30 million fewer words than their more affluent counterparts. That “word gap” reflects a general lack of school readiness that affects performance in the early grades, which then sets students on a less successful path through middle school, high school, and life.

A desire to interrupt that process of replicative injustice is what has driven the effort toward universal pre-kindergarten (UPK) for 4-year-olds, a cause New York City Mayor Bill de Blasio famously adopted during his 2013 run for mayor and implemented citywide in less than two years, an achievement for which his many detractors rarely give him credit. Seventy-thousand children—more than in the entire school districts of Boston, San Francisco, or Atlanta—participate in that program.

Now de Blasio is proposing to chase educational inequalities even further back toward the delivery room. At a school in the South Bronx on Monday, the mayor laid out a vision for establishing citywide preschool for 3-year-olds—universal 3-K—by the year 2021.

“Every child needs to be reached, every child needs to get the strongest possible start,” the mayor said in a school gymnasium at PS 1 in Morrisania, where more than a quarter of students are considered English-language learners, roughly one in five have some special-education need, and the school’s most recent state-test scores—18 percent hit grade-level proficiency on English and 11 percent on math—fell well shy of the citywide average of 39 and 40 percent, respectively. “We have proven through the growth of pre-K that it can be done and it can be done quickly. We have proven that it can reach every child, and the evidence is overwhelming of the impact it is making on children and their schools.”

“We know there is a precious opportunity to reach children at the moment when they can learn and grow the best,” de Blasio continued. “The fact is the most important development of the human mind occurs before the age of five. Parents see it and scientific research confirms it. There is one opportunity to get it right. This is the opportunity we have missed throughout our society for generations.”

“3-K for All in NYC” will be the largest such program in the nation—a “game-changer” according to the mayor. But he warned that pulling it off will be harder than pre-K was.

The effort will start with a focus on the 10,000 or so 3-year-olds who already get early-childhood education through the city’s means-tested Early Learn program. The new investment will provide increased family support, improved teacher training, and a better curriculum.

Next, the administration will provide 3-K for all in two districts, Morrisania in the Bronx and Brownsville in Brooklyn, that have particularly pronounced needs. The city will at the same time launch a survey to find space for the broader program, look to recruit nonprofit providers, and find and train teachers. By 2021, the de Blasio administration will implement 3-K in eight other school districts, serving some 20,000 students. By then, the administration also hopes the state and federal government will have agreed to pick up the cost of expanding the program to the remaining 21 school districts to achieve universal, city-wide 3-k.

All told, the annual cost of the scaled-down program to the city by 2021—the final year of de Blasio’s second term, if he is reelected in November—will be $177 million, on top of the $200 million already spent on Early Learn. In order to serve the 62,000 or so kids who would enroll in a full program, the city says it will need $700 million more from the federal government and the state each year—meaning the program will cost more than $1 billion.

Unlike UPK, which ramped up quickly, 3-K won’t become universal until four years from now. City Hall says that’s because UPK has gobbled up so many qualified early-childhood teachers that it will take time to recruit and train enough 3-K teachers. Some 4,500 will be needed.

It’s worth noting that, like UPK itself, 3-K potentially has two sets of direct beneficiaries: the kids who get the program, and the parents who get at least some free, high-quality child care during the day. Cobbled together with other child-care resources, that could allow more low-income parents to work, bolstering family finances. Parents who right now spend an average of $10,000 a year on day care could save that money.

One criticism of the current UPK program is that, by virtue of its being universal, it also spends public money on affluent children who don’t need it. By devoting city money to prioritizing rollout of 3-K in the districts with the highest needs, de Blasio is proposing a better-targeted program this time—until it transitions into a citywide program. De Blasio said, “I believe fundamentally in the universal model. I think it is good for everybody. I think it creates equality in our society. I think it creates a communal reality. It obviously creates maximal energy to get something like this done. I believe the mix of different people lifts all boats.”

The mayor’s plan was enthusiastically embraced by people who joined him on the stage at PS 1. City Council Speaker Melissa Mark-Viverito called it “truly visionary” while Council Finance Committee Chair Julissa Ferreras-Copeland said, “The mayor is really thinking about wrapping our children with every tool, every protection necessary.”

“A three-year-old is a sponge. They pick up everything. So why not have them in the right place, where they pick up the right stuff?” argued Schools Chancellor Carmen Fariña. She said 3-K would allow kids to learn to share, cooperate, collaborated, critically think and analyze, give teachers a chance to identify learning disabilities and speech issues earlier, support parents at a critical stage, and make schools more deeply engrained in community life.

3-K is just the latest “big idea” by de Blasio, whose reelection prospects look rosy but who was criticized just a few months for lacking a defining cause to animate his second term. That was before he promised to create 100,000 good-paying jobs, end the use of private apartments and hotels in the homeless-shelter system, close the jail complex on Rikers Island, and now expand the UPK idea to all 3-year-olds, on top of his push for a Brooklyn-Queens streetcar.

Some of those ideas have ended up looking smaller on second glance. Little distinguished the 100,000-jobs plan, rolling out over 10 years, from existing policy. The homeless plan entailed an ambitious plan to build new shelters, but not a game changer like creating more permanent affordable housing for the homeless. Rikers’ closure would take a decade and hinge on a continuing fall in crime. And the financial rationale for the streetcar is looking a little shaky.

The 3-K idea is vulnerable to the same kind of “yeah, but…” critique. UPK itself is still so new that there’s been no public distillation of lessons learned about what works and what doesn’t, and there have been implementation wrinkles that might not be well enough understood to avoid repeating with 3-K. And adding a new program for younger New Yorkers does nothing for the kids already in the school pipeline, an area of education policy where—for better or worse—de Blasio has not showcased his ideas as much as his predecessor, Michael Bloomberg, did.

Some raise questions about the universality of the idea. “There is national evidence that when poor kids enter pre-k at age 3 and attend for two years, the cognitive gains are stronger, but this finding does not hold for middle-class kids, as far as we know,” says Bruce Fuller, an education expert at the University of California Berkeley. “The mayor’s new thrust may be great urban policy, holding middling families in the city, which benefits others. But after hundreds of millions of dollars, do we know whether the mayor’s program is propelling kids?”

The biggest challenge raised by the mayor’s 3-K plan, however, is that full implementation depends on state and federal budget support. De Blasio’s efforts to secure state backing for UPK in 2014 turned his simmering rivalry with New York State Governor Andrew Cuomo into a barn burner, and the mayor’s push for a Democratic state senate in 2014 not only failed but triggered an investigation, so it’s not like he can count on getting help from. De Blasio said he’s confident that, as the program expands on the city’s dime, the case for help from the state will get stronger.

On the federal side, where the city is facing devastating cuts to security and housing funding, the likelihood of more support from the Trump administration and a Republican-dominated Congress for another big-government program seems low. De Blasio is counting on a growing bipartisan coalition behind early childhood education and/or a huge swing in the 2018 state elections and federal midterms, as well as the 2020 presidential contest. “We’re talking about September 2021 and a lot can happen by then,” he said.

The mayor’s political instincts about Hillary Clinton’s shortcomings were sound in 2016. New York City’s 3-year-olds will have to hope his sense of Trump’s shelf life proves just as prescient.