Here are some options for your situation.
You could look for an investment partner who will put up some or all of the cash in an equity-sharing partnership. You make the monthly payments and the two of you split the eventual resale profits.
Get owner financing or a land contract. Another option is to have the seller act as the bank. You make your payments, including interest, directly to the seller. Then after usually 3 to 5 years you make a lump sum payment to the seller. During this time, you should have enough equity to qualify for a bank loan.
If you have a primary residence, you can also use a home equity line of credit from that property. If you have equity in another property, you could use that equity as a down payment on purchasing another investment property.