So here goes the post from someone who once was in your shoes:
YES there are ways to become an officer from the enlisted side, actually there are several. Below are the various paths:
1. STA-21 - Seaman To Admiral: Throughout the pipeline, you will be able to apply for the STA-21 option. Usually about 30% of those who apply, get it. However, it requires a very demanding GPA from both NFAS and NPS. While STA-21 will be offered to you when you hit the fleet, the best time to apply is earlier in the pipeline.
2. OSC - Officer Candidate School - Typically, correct me if I'm wrong, this requires extensive knowledge and technical expertise. So, given that, usually it is only offered to well qualified sailors, such as Chiefs. My SLPO (Section Leading Petty Officer), made ensign through OSC while I was still at NPS.
3. Warrant Officer - This is a unique rank, and requires only the best of Chiefs. Don't expect this to come easy, nor towards the beginning of the pipeline.
4. Naval Academy - This is where my role comes into play. I was accepted to the Naval Academy while still in NFAS, but didn't leave until well into NPS. (Over 2/3rds into it.) Typically the pick up rate for this commissioning program is about 60 - 70%, but requires extensive patients and paperwork to be filled. If you want it bad enough, I would definitely say the Academy is worth it. However, you will be quite tested, and it might be difficult moving from rank to nothingness.
I'm sure I'm missing one or two in there somewhere, but give it some thought before making any moves. I would suggest doing extensive research, even if it might cost a few hours of your time.