About 65,000 undocumented students — students born outside of the United States who are not U.S. citizens or legal residents — graduate from U.S. high schools each year. An estimated 5-10 percent of these students go on to college. While this is a low number percentage wise, it nevertheless respresents between 3,250 and 6,500 college students year over year. So, while it is not necessarily easy, it can and is being done in the US on regular basis.
The added complication in this case solely is the non-tax filing status of the parents. @RecursionRecursion google “Colleges that Meet 100% of Financial Need for Undocumented Students in 2019-2020”, which will provide you with a comprehensive list of respective US Colleges with their applicable policies. The key to success will be to identify colleges where you have a realistic chance to actually be admitted and which will subsequently work with you on acceptable “Non-Tax Filer Statement” documentation, which can not come from the IRS in your specific case. Financial Aid Offices of those colleges mentioned above are well acquainted with your challenges and will be able to advise you accordingly. Prepare a short list of colleges and call and speak with them individually.