I don't see an official Polymer Datepicker component. A quick web search yields the following third party components. One of the below thread has some interesting tidbits. Can we expect an official one in the coming weeks?
I've created paper-date-picker (docs / demo) and paper-time-picker (docs / demo) components with the goal to mirror the android versions as closely as possible, while still having decent performance on mobile devices. I opted against infinite scroll for the date picker, as I couldn't seem to find a way to make it work without sacrificing performance.
Please test on your own devices and let me know what you think (pull requests welcomed)!