This is what's frustrating with Google's Material Design. If tech-savvy users like me can't even find or know that the year is clickable, what hope do most non-technical folks or seniors have?
I noticed a fair amount of complaints about this in the thread, so am sorry for the poor experience.
In an attempt for simplicity I used a simple <input type=date> field which means it uses your OS or browser’s native date picker. As a Mac/iOS user I’m pretty familiar with those, but I’ll admit I did not test this across Windows or Android devices which apparently have not done a great job at this UI element.