Problem with the brrrr method

[Cooper Dunnavant]

I am currently looking for a house to start my real estate investing portfolio, and was planning on using the brrrr method. I've got pre approved for a loan and have extra cash saved up. The problem I'm running into is the amount I'm pre approved for is the max income to debt ratio the bank is allowed to give a loan out for, to individuals (43%), which is fine because in a perfect scenario as long as the property is cash flowing every property bought will lower your income to debt ratio, making it possible to keep buying property's. What the loan agent at the bank said is they don't count rental income until it's on my tax returns for two years, making it impossible for me to buy a second property and so on, without exceeding the max income to debt ratio. Should I look for another bank or what other financing options do I have.