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
"Sync Project with Gradle Files" is not present in IntelliJ. However a similar option is available to build all the gradle files together. Go to View --> Tool Windows --> Gradle. A Gradle task panel gets displayed in the right side with the list of apps. Select your app and click the "Refresh all Gradle projects" in the top bar of the Gradle task panel.
Another method is as mentioned by "Avi Arro"