You Can Install the June Update Right Now
If you don't want to wait for the June Android 7.1.2 OTA, you don't have to.
Google's updates typically take a week or two to fully deploy. So if you're dealing with an unfixable issue or you simply want the new security patches right now, you might want to manually install the June build (buildN2G47W) right now.
Google's released factory images for the latest version of Android 7.1.2 Nougat. The Nexus 5X's June update is now available via the company's website. (Full OTA images are right here.) If you know how to sideload software, dig in.
If you aren't familiar with the manual installation process, we've put together a sideload guide that will take you through the necessary steps. Once you get the hang of it you should be able to sideload future Android updates on your device.
If you don't feel comfortable with the steps in the walkthrough, you'll want to wait for Google's OTA to arrive on your device.