There's a quote I read once, and I wish I could find the original source so I could provide a proper citation, that I think was from Bob Parsons that goes "Never be afraid to enter a crowded market. Just be better than everybody else." That might be a little bit hyperbolic, but I think the general attitude is sound. Don't be afraid to get in there and mix it up and compete.
As the old saying goes "Startups don't die by murder, they die by suicide." Most likely, the other startup you're think about is going to die by suicide anyway. They're going to fail to execute, choose a bad market segment, screw up their marketing, screw up sales, choose SVB as their bank, or any of 1000 other things that are going to send them to the Great Accelerator In The Sky. Just don't make those mistakes, outlast them, and the market is yours!
Steve Blank[1][2] also has a lot of salient advice on these topics.