Is there a way I can get Paraview to make use of my many cores instead of just one?
ParaView is multithread and uses all the cores of your machines when it can, which is not always the case.
That being said, you can also work with parallel server, see here:
https://www.paraview.org/Wiki/Setting_up_a_ParaView_Server
Or maybe even use my Geforce GTX 1060, which should be quite quick?
ParaView is using your GPU for rendering and for computation in some cases depending of your configuration.
But it always takes ages to render all the calculated time steps into pictures to later process them to a video for further engineering in the team.
To get proper help, you will need to be more specific on what is taking ages and how you install/build ParaView.