Jacquelyn, interesting question. For the first couple of internships that I had I was in a similar position that you find yourself in; not a ton of work experience and nothing that really demonstrates that you have a background in the job that you are applying for. The good thing is that since this is your first job, Publix most likely expects this to be the case, meaning that Publix most likely doesn't expect the people that are applying to its job opening to have ten years of relevant work experience.
If you don't have any work experience, try to put down any community engagement that you have been involved in, volunteer work, part time jobs, really anything that shows you are a human being who is good worker. Do stress out about this too much as it is understable that you lack experience given that that is your first job, everyone has been in your position before. I hope this helps and please feel free to ask a follow up question should you have any.