It is possible to control the camera within Fusion. This defines what you see in the current view. Here's a blog post I wrote several years ago describing cameras in Inventor. All of the same concepts apply to the camera in Fusion. Here's a response to a previous question on this forum with some code that rotates a camera around the origin. Hopefully, both of those will help.
It's not currently possible to access the View Cube functionality, but it's not needed if you just want to control the current view. Where the View Cube might be needed is if you want to know what direction the "Top" or "Front" is. The is defined by the view cube and can be changed by the user.
---------------------------------------------------------------
Brian EkinsInventor and Fusion 360 API Expert
Website/Blog:
https://EkinsSolutions.com