You've focused on what you do not have, so it is time to focus on what you have. You have seven years of employment experience. If it is with one or two employers that demonstrates stability and staying power. If you have good evaluations and could produce positive references, that is another thing you have. You have a Bachelor's degree in a relevant field of study and that is another selling point. Does your resume reflect these positives? It should.
Plenty of people get ahead in the security industry without law enforcement or military experience or knowledge of information security. Some of them started out as security officers so there is a way forward. Your drive and determination will impact your success in climbing the ladder. The first thing you should do is obtain the PSP (Physical Security Professional) certification through ASIS. Since your employer won't pay for training, invest in yourself, and get the certification. That should demonstrate you are serious about growing as a security professional and that you have the core knowledge for a role with greater responsibility. While you're preparing for the exam network with ASIS members in your study group and local chapter to learn who is hiring and make connections that can help you find that next step up. Connections are invaluable. Your goal is achievable!