I found the follow note, which describes exactly what I'd like to do:
Note: If your users are only uploading resources (writing) to an access-controlled bucket, you can use the resumable uploads functionality of Google Cloud Storage, and avoid signing URLs or requiring a Google account. In a resumable upload scenario, your (server-side) code authenticates and initiates an upload to Google Cloud Storage without actually uploading any data. The initiation request returns an upload ID, which can then be used in a client request to upload the data. The client request does not need to be signed because the upload ID, in effect, acts as an authentication token. If you choose this path, be sure to transmit the upload ID over HTTPS.
https://cloud.google.com/storage/docs/access-control#Signed-URLs
However, I cannot figure out how to do this with the Google Cloud Storage Library for Java.
https://developers.google.com/resources/api-libraries/documentation/storage/v1/java/latest/
I can't find any reference to resumable files, or getting the URL for a file anywhere in this API. How can I do this?