They can see the timing and packet size for your requests to the VPN server, as well as what your VPN provider is. On the VPN's end they can see what sites the users (collectively) are visiting, the packet sizes, and the timing. That information alone is enough to identify who is doing what with reasonable accuracy.

This is before issues of using the government's massive resources to brute-force encryption, possible government backdoors in VPN servers, and browser fingerprinting.

There are various steps that can be taken to mitigate this, and this of course assuming the government has access to the ISP's metadata from both your network and the server's network (not a stretch, but not necessarily guaranteed).