Without proof of income, you’ll be considered a very high-risk candidate by most lenders. Lacking this documentation will make it difficult to find a lender willing to hear you out.
To put a lender’s mind at ease, you may have to put a large down payment, perhaps 20% or more of the total cost. You may also be subject to higher interest rates (again, due to your high-risk classification). If you’re approved, double-check your final contract for any hidden fees.