I don’t know if this is how it works in other states, but my state you can sponsor yourself to go through the police academy before getting even applying for a law enforcement job.
If you sponsored yourself to the academy, and excel academically and show great aptitude in everything, could it help you to get hired?
In my state the academy is more like a certification program. You need the certification to be a cop, but completing the academy does not get you a job.