While in school working towards my BA in Business I met a property accountant who was in my class. They got to know my work and they were aware that I was looking to get into ANY entry level accounting job. That person got a promotion but needed to fill his position first so that's where I came in, I got a high recommendation and that was all that was needed as they needed to fill to position ASAP. I don't think you need an educational background, it would depend on the company. There was another Jr. Property Accountant at the time and they had a degree from a culinary arts school, they were referred by another employee, started doing AP then property accountant now they are an assistant property manager.
Best thing I can recommend if you don't have a business background is to start at an entry level admin job at a Property Management firm, let everyone know you want to be a PA and hopefully you'll get cross trained and a position opens up.