Google Cloud Platform offers four hosting options for Java developers. It's important to consider which environment is closest to your needs, but also keep in mind that many apps will need to take advantage of two or more of these hosting options.
Google App Engine is a great place to start. App Engine is a platform-as-a-service for web applications and mobile backends. It can automatically scale your application in response to traffic. There are no servers for you to provision or maintain. Alternatively, if you're interested in using virtual machines or containers directly you can jump to the tutorials on using Compute Engine.
App Engine has two environments: the App Engine standard environment and the App Engine flexible environment. Each environment has tradeoffs. You can read about the general differences between the two environments in the App Engine documentation. For Java developers, the key differences are described in the table at Java on Google App Engine.