If you don't have advanced projects (ie. only Basic Projects), the menu doesn't show projects as a standalone options - normally you would create a project from a customer.
However, you may have noticed when you do this, the URL contains &parent=xxxxx being the ID of the customer.
If you remove the parent=xxxxx, and just have:
Add this as a browser bookmark or NetSuite shortcut.
https://xxxxxxxxxx.app.netsuite.com/app/accounting/project/project.nl
Then the new project screen opens and customer is blank (and not mandatory).
It should be noted that the project is an pseudo entity, but not a transactional entity (it won't be available to use for sales orders etc.). but you can use it to track time against the project if you have enabled time sheets.