I am an attorney. Besides having a regular law degree I also have a Masters of Law in Taxation. Do not take this as creating an attorney-client relationship. However, you may find my opinion helpful.
If you are not getting meangingful answers here, the trouble with your question as phrased. When you say you are only paid in cash, are you talking about steady employment or, instead, are you someone who does work for various people and are paid in cash.
Most of the other posters are assuming that you have a regular job with one employer. If so, it would be unusual for your employer to pay you cash, but even if your employer did so, there should be a Form W-2 (not a 1099) stating your wages, the amounts withheld for taxes, etc. That could be used to prove income. If you are getting paid “under the table”, that would be a tax violation for your employer and you. Also, as others have pointed out, it would be difficult for you to prove your income for something like qualifying for a loan.
However, for all I know, you may just be providing services to various persons for cash. Just this morning I paid the farrier who put shoes on my horses. Last year I hired several people who were out of work to help me with various projects on my property. These were working as independent contractors, not employees. As a private individual, hiring services not related to my business, I was not obligated to withhold anything from the income of any of these people nor was I obligated to give them a Form W-2 or Form 1099. It is up to them to report their income.
If you are in business for yourself, giving services to various persons, you need to set up a system for keeping good records of cash receipts and bank deposits. Any certified public accountant can help you with that. You can then report taxable income, business deductions, make quarterly tax payments, and establish a legitimate and credible income history which can be used for other purposes, like applying for a loan, credit card, or renting an apartment.