I just added the google-play-services-lib library to my project and am stuck where I need to \"sync the project with gradle files\", but this button does not exist
There is a useful shortcut Ctrl + Shift + A, after which a window appears and you can type some command that you would like IntelliJ to run. Just type "sync" in there and it will find that command Sync Project with Gradle Files, even if it's not visible in the menu.