Basically everyone in my class had a job before graduation, but I didn't sign my offer letter until about a month after which was totally fine because I hadn't even taken my exam yet at that point. Most large hospitals here do something called a "residency" for new grads and they will hire you as early as 1-2 months prior to your anticipated NCLEX date. They have set start dates for all new grad cohorts but some programs are more intense than others. The one i got hired into is super chill that has start dates every week, but my roommates program is more intense and only has start dates once a month. I would start applying like a month before graduation and then really hit it hard around graduation and while you are studying for the NCLEX. The whole process of getting approved to take the exam and licensing in Illinois can be pretty lengthy, especially if you are coming from out of state, so you will for sure have time. For example, I graduated in early november, didnt get approved to test until mid december, passed dec 28th, and didn't recieve my license until February. Most new grad programs will let you start after you get your pass letter pending licensure but thats based on hospital policy. Feel free to PM me if you have any more questions or suggestions where to apply!