I used to have these feelings as well.
I'm soon to be jumping into a crowded market as well. Many of my competitors have had VC funding and do billions per year.
It doesn't bother me in the slightest. I can be far more nimble than they can. Doesn't matter if they try and stomp me. A bigger company will always do something in their own interests and piss off a segment of their customer base which means they will move eventually.
Not only that, because I don't have VC funding. I can always have lower prices CapEx and move it OpEx instead. As long as I am much lower costs compared to being with the incumbents then it's a better prospect cost wise to my customers.
Finally, better customer service, features, ease of use, pricing and roi to the customer is what matters at the end of the day. If you simply have a much better product and able to generate and retain trust in your user base. You'll be alright.
My advice. Just start the business today. Whether or not you get stomped on is neither here or there. What matters most is the experience you'll get vs in 5 years time when you wish you had started and still scared!