Startup culture question RE: unit tests

If you are at a startup, you need to fail fast, do rapid iteration, and deliver something to the customers to test. Usually then the need to write unit tests falter.

Usually at a rapid iterative setting, unit tests are a hindrance, a nuisance, yet another thing to maintain.

Assumptions: Let's say your team is a mix of vanilla juniors and associate ~ senior level developers. Let's also say the routine is to test out their code so it doesn't break, and then further testing is left onto the QA team, and they are bemoaning the pressure of testing without full specs and need to QA in very short timeframe. Juniors have never been exposed to writing unit tests.

Question: Can you share your thoughts/experience on this? What is the role of unit tests – and can they be ignored for some phase in the life of a startup, at least until the product matures? If not, how did you start introducing in unit tests and still stay have product/sales/marketing be okay? How did you keep the development stay nimble/agile/rapid?