This will help your applications quite a bit.
You can get this at quite a few universities.
At the most famous and highest ranked universities such as MIT and Columbia, there are a very large number of research opportunities. However, there are also a very large number of very smart students. It is hard to stand out.
I have a daughter who attended a small university in Canada. Since it is both small, and in Canada, you have probably not heard of it. She was one of the stronger students, and quickly got to know her professors. This helped her to get very good research opportunities. After graduating she returned to the US, and relatively quickly had three job offers. Because she was interviewing during the pandemic her interviews were via zoom, so I actually got to hear a few of them from the next room. They got into a great deal of detail regarding what she had done while doing her research in university.
Also a lot of universities offer coop and internship options, where you might for example work at a company or work at a nearby research facility over the summer or while taking a semester off.
So there are research opportunities at a wide range of universities, both in the US and in other countries.
This does lead to the question of how you judge the extent of research opportunities at each university. I am not sure that I have a good answer to this question.
If you are the strongest student in your high school, then applications to MIT and Columbia makes sense. However, you definitely need to apply to universities where admissions is more likely.