Indulgent Emotion

I’ve been defining a niche that I would like to use for my business. I did a lot of research and couldn’t find anyone with the same niche and offering combination. There are similar business but different enough that I felt like I could offer something new and fill a missing need. Well, I recently came across someone doing the exact niche I had in mind and she basically solves the problem(s) I planned to solve for my clients. I notice myself thinking that no one will want to work with me when they can have the same thing from her (who has more experience, is well-established, is well-known, etc). I feel defeated and I know I’m indulging in this. Intellectually I know that my service and brand won’t be identical because I bring my own experiences and perspectives, but I’m worried it will be too similar (and no one would pick me over her). Can you help me move through this?