Some of the very youngest and most promising New Yorkers are getting the classroom door shut in their faces.

Of the 14,483 incoming kindergartners who took NYC’s Gifted & Talented exam this winter, more than 4,500 — or 31 percent — qualified. But there are only about 2,500 G&T seats for those children.

To choose the lucky ones, there will be a lottery. The educational paths of thousands of 4-year-olds will be determined by pure chance.

But in four neighborhoods, the city is offering a different option that might open new doors. Education officials announced plans to create new G&T programs in the four school districts in the Bronx and Brooklyn that, until now, had none. They will start in third grade and won’t admit students based on test scores, but instead on attendance, report cards, and a qualitative analysis of “gifted behavior indicators” that range from whether a student is curious and motivated to whether he or she is a “fast learner.”

The city’s plan to reach previously ignored districts is a good one, no matter how late in coming. And waiting until second grade to determine eligibility will allow a broader range of children to qualify. All students in the four districts automatically will be considered. This is a new beginning in NYC gifted education and should be carefully evaluated.

But education officials must watch out for pitfalls. Previous subjective screening efforts, at times, were accused of bias against minority and low-income children, and that must be avoided. And the third-grade start for gifted classes makes the earlier years, from pre-K up, even more important; no one should be left behind.

There are gifted students in every NYC community. To reach them, education officials have to do even more. Test every pre-K student for the existing programs that start in kindergarten, unless a parent chooses to opt out. Add more kindergarten seats in high-need areas. This is a chance to create a more level playing field, and to meet the needs of every student in every neighborhood.