I am starting a SaaS product with a proven market (competitors or similar products that already exist).
Now the problem is having a big potential market, how do you find your initial niche market and have initial focus?
Positioning. Positioning. Positioning.
If you can't create your own product category, and instead customers immediately pigeonhole you into "how are you better than XYZ?" I'd say you're in trouble.
Call your product something different. Offer a different value proposition than your competitors. Go Blue Ocean Strategy on this.
I'd highly recommend GrowthRamp.io and also of course April Dunford for further reading.
Search relevant sub reddits for keywords like: app, software, product to see what problems people have and categorising them by niche.
Price, quality, and service are your three value drivers.
Self-service tools usually appeal to customers that care about price, primarily.
Look for markets where competitors are heavily funded and can't offer the flexibility and pricing that a self-serve tool could offer.
We're too in a crowded/proven market (which I see as an advantage) with Sidemail.io and I think doubling down on what makes your product stand out is the way to go.
For example, we recently added data charts you can embed into your transactional emails. There's a lot of website monitoring tools that could easily make sending an email report with uptime inside of a nice chart their own selling point.