I am a 15 year police officer. I am in central Florida. Many applicants in this area start at a smaller LEA and then after 2 years or so (some even less) apply at a larger agency.
In my area, larger LEAs tend to require college to get in the door from applicants with no direct LE experience (Tampa FL does last time I checked). With others LEAs, you need a degree only if you want to make rank. Sometime the LEAs change their requirments becuase they are short of manpower and need more applicants.
As long as you have a pretty good personal record, and you don't mind starting at a smaller size LEA you should not have too much of a problem eventually getting to a larger LEA.
Most agencies have recruiters that you can talk to before you apply to see what that LEA likes their applicants to have. LEAs tend to be like people, some want different things than others.
The sherrif's office in my location under the last Sheriff really liked prior military guys; the current one really likes guys with college-altho it is not a requrement to have a college degree or prior military.
Hope this helps,
Nothing is impossible for the person that doesn't have to do it.