Definitely possible, but you will need a virtual device to act as the trigger for an Alexa routine (not a SmartThings routine). This is a very popular kind of use case and a lot of people use it.
So you put whatever logic you want on the smartthings side like time of day, etc, and use that to control when you turn on the virtual device that will trigger the echo routine.
So in the echo routine, that virtual device turning on is the “if“ and you will use “announcements“ in the routine for the “that“ to speak your desired phrase from your desired echo devices
See the community – created FAQ for the details:
FAQ: Can I trigger an Echo Action without Speaking to It?
You will need to use an edge Driver for the Virtual device once the transition to the new architecture is complete, and the FAQ includes a link for one of those if you want to go ahead and get started with that method.