So the Trimble Sync page says this:
Can I create a new project in Trimble Connect Web?
No, to maintain the correct relationship and file structure between Trimble Access and Trimble Sync Manager, you must create projects and jobs using the Trimble Sync Manager desktop application. (link)
So based on that, is there a way to create a template project in Trimble Sync, and use it as a template to create other projects? You can create the folder structure needed in Trimble Sync, but I see no option to copy the Sync project. You can open the project in Trimble Connect Web and copy it to create another project. Except the folder structure does not copy over.
As a work around, I created a batch file that the survey crews can run on the TSC7 which will create the required folder structure within the project folder. How is this not a feature of Sync??