You can try going thru your county, city or state and find out if there are down payment assistance programs or grants for first time home buyers. I believe they exist in all 50 states, however, requirements vary based on income, credit and whether you need to take a home buyer class. Also the down payment amounts vary depending on your state, city our county's budget.
Another option for down payment is family members who can gift you cash for a down payment. The family member will need to complete a gift letter stating the money is not a loan. Finally, there is your retirement savings account. I do not recommend withdrawing from your retirement account but it is a source for down payment. You will pay a penalty and income taxes on any amount withdrawn.
The only 2 options for $0 down payment is if you served in the military and are eligible for a VA loan or if you are buying a rural property and eligible for the USDA loan.