As a former State Farm claim rep, I can speak to how it used to be. Do not take this as gospel for what I like to call (sometimes with scorn) "The New State Farm".
In years past, State Farm actually preferred to hire claim reps with little or no experience so they could be taught "the State Farm way". Again, in years past, soon after they hired someone, they sent that person to a two to three week State Farm Claim School that was very intensive and an excellent claim school. The last time I worked alongside a State Farm catastrophe team they were far from seasoned and experienced professionals.
Many of the cat team "reinspector/trainers" had State Farm Claim School (which I admit is excellent) and little more to their credit. Being myself a graduate of said school, I could sometimes explain the coverage to the "reinspector/trainers", and sometimes I just was unable to assist them to "get it". I remember well the time the tornado blew an object against a wall without making a hole in the wall, and it knocked over a television up against the inside of the wall. The cat supervisor was an auto supervisor who wanted to do something different for a change and the "reinspector/trainer" was a recent claim school graduate. The supervisor saw I was recommending a payment on a content item inside the home with no hole in the wall. The "reinspector/trainer" also knew next to nothing. Between them they took me to task. No amount of explaining that the hole in the wall provision only applied if the television was damaged by rain, snow, sleet, sand, or dust could prevail against this dim duo. Oh well, that's water ten years ago under the bridge. I did get the insured paid for the television, but not without the help of my vendor cat supervisor explaining their policy to them as well.
So, it's worth a try to get on with State Farm. They will train you and you will meet some of the truly good people who work for them. Just don't assume that everyone knows what they are doing, and you should be alright.
If you cannot find employment opportunities on their website, I would start by contacting the nearest State Farm agent and tell them what you want to do. If they cannot help you, they can direct you to the regional office where the human resources department should be able to point you in the right direction.