If you have the money for closing costs and deposits, what you could do is instead is use the funds you have for the closing costs and deposits for a down payment. Then you get what's called a "sellers concession" and use that to cover closing costs.
FHA only requires 3.5% down and they allow you to get a sellers concession for 6% of the sale price.
So if you are for example buying a house for $100,000 you would be allowed up to 6% ($6000) as a sellers concession to use for closing costs. So $6000 gets credited to you to use for closing costs. You would then need 3.5% down payment ($3500).
As another option there is 100% financing available through a USDA loan. There are income restriction and area restrictions on these loans.
I'm a mortgage professional. If you have any questions or need any help you are welcome to contact me. I'm available almost 24/7 and can lend nationwide.