This article almost uncovered the real point of the class gap and education, but missed the mark IMHO.
I know nothing of New York, but I have a hard time believing their are no free/low cost opportunities for kids. My relatively small city is full of options, but as a parent I have to know how and put in the work to find them and take advantage of them. Personally, I think my kids would have less opportunities if we had opted for the expensive preschool/private school route because they wouldn't have had time for everything else they do.
As younguns, we had museum groups, where we took advantage of free museum days for group field trips, we had community camps and classes that were inexpensive (or free if your income was low enough), we went to free monthly kids classes offered by adult hobbiest groups (astronomy, rocket clubs, art clubs, outdoor clubs). Library groups and classes, reading clubs, playgroups. They were all available if you spent just a few minutes searching online each week.
Now that they're older, they belong to some of those adult hobbiest groups, even though they are often the youngest members. Heck, my 8 year old has befriended a retired astronaut and a physics professor through his astronomy club (cost for membership: $25 a year. Benefits: Meetings, lectures, classes, free telescope rentals). If he maintains these relationships, he'll have some awesome reference letters come college application time. That plus the hours and hours he puts in each month doing astronomy outreach and teaching at schools and community events should make any application he sends in stand out a bit. No fancy preschool required.
The problem is that many middle and lower income parents depend too heavily on the public schools for all things educational, while higher income parents know you have to actively search out the best opportunities. There are opportunities available for all income levels, if the parents are willing to put in the legwork to find them and the effort to take advantage of them. Sure, it may be easier to find good ones with a higher income, but no one said that life was going to be easy.