If you are asking whether you can file an income tax return without a Social Security Number or a similar number issued by Mexico or Canada, the answer likely is "yes" but the filer must take additional steps to submit the return. In general, the IRS requires every taxpayer and dependent to have Social Security Numbers.
If you are asking whether you must submit a driver's license, passport, or similar ID, the answer depends on whether you already have a SSN or similar number from Mexico or Canada and whether your tax preparer are willing to accept you as a client if the preparer cannot verify who you are.
If you do not already have an SSN, ITIN, or similar number from Mexico or Canada, you must provide certain documents to get an ITIN.
Given the number of scams, many tax preparers want to verify who a person is to avoid being used by that person in a scam.
You should review the specific facts with your tax preparer to see what options you have.