Every software project takes time before its requirements and design stabilize. A classic comparison is between the UI that can change at any time in an application's lifecycle and back-end services that may live untouched for generations. Agile projects behave differently from waterfall in this respect. If you're developing a SaaS product, you must use automation to support frequent deliveries, but you'll have to carefully consider the effort you invest in developing tests because your requirements may also change frequently. This a fine balance you'll have to learn to work with. For an on-premise solution, it may be easier to identify the stage in which automation tests can be safely developed and maintained. For all these cases, you have to carefully consider when it's cost-effective to develop automated tests. If you start from day one, you'll expend a lot of resources shooting at a moving target.
I think we can all agree that automation is a critical part of any organization's software delivery pipeline, especially if you call yourself "agile." It's pretty intuitive that if you automate testing, your release cycles are going to get shorter. "So, if that's the case," you might say, "why don't we just automate everything?" There's a good reason: automation comes with a price.