At its core, an early stage startup's only goal is to create business value as ruthlessly as possible. Let's talk about how I apply this principle to my testing strategy.
Do automated test suites help create business value? Absolutely, I no longer have to test everything after making a change. Your application is going to be tested, either by you, or by your users.
Does having a well defined layout of UI, service, & integration tests, a-la Martin Fowler add business value? I would argue it does not. I write mostly integration tests, because you get more, 'bang for your buck', or 'tested code per minutes spent writing tests'.
Does this testing strategy create tech debt? Absolutely. I view this as a good thing. I am causing problems for myself in the future, in exchange for expediency in the present. Either my company grows to be successful enough to care about these problems, or we go out of business. If we become successful enough to care about rampant tech debt, hooray! we are successful. If we fail, it does not matter that we leveraged tech debt, we still failed.
Writing good code is an art. There are people out there who are incredibly talented at writing good code that will be battle-tested, and infinitely scalable. These are often not skills that an early staged startup needs, when trying to find product-market fit.