The NYT summer program should be a valuable experience in many respects such as getting to know NYC, meeting other journalism students & professional writers, and gaining knowledge about journalism and writing as a career.
You appear to be pursuing your passion in high school and that, along with excellent grades and an outstanding SAT score, should be enough. But, since you asked for suggestions, consider entering writing competitions for both poetry and prose.
I have relatives who are professional writers. The two most recent (both majored in math during their undergraduate years) attended Columbia’s journalism school masters degree program. For writing Northwestern University is among the world’s best for undergraduate degree in journalism and Columbia is among the very best in the world for masters degree programs in journalism.
Any connections made with NYT writers, editors, & publishers can help.
Several other US colleges and universities have strong writing programs and some MFA (Master of Fine Arts) programs are free to those accepted if willing to assist with teaching/instruction duties.
Do you have an specific area of interest in writing ? If so, this can be a positive aspect for college applications,although it’s okay to experiment and specialize in a master’s degree program.
P.S. Since you did well on your Micro & Macro AP tests, double majoring in economics and journalism can help with defining your career goals and securing employment as a writer.