For someone with no experience actually working as an on-site manager, your best bet is to focus on getting hired at a small complex where you only get free/reduced rent. Bigger complexes or ones that provide free rent and a salary are only going to want experienced people with a track record.
The best way to get the attention of a small complex landlord is to have experience in making minor/small repairs and doing maintenance. Such landlords usually do not have their own handyman on staff and only want to pay someone to make specialize or major repairs (plumbing, electrical, etc.). Basically, it really helps to look like you are your own handyman because most small complex LLs expect their on-site managers to make such repairs themselves.
That means being able to repair drywall, know how to do interior paint (including which to use), caulking, replace smoke detectors, replace locks, swap out P-traps, change out light switches, repair/replace toilet guts.... basically almost everything someone who owns his/her own house would try to do or do themselves. It also helps to own your own tools, owning your own truck is a HUGE plus.
If you don't know how to make such repairs, learn. While you might not be able to get such experience doing such repairs (or at least not quickly), you can quickly teach yourself HOW to make such repairs and that will come through when you interview.