I use a machine where I don't have administrator rights. I've been able to run programs without admin rights by extracting the program's .zip file to a directory I have created on my desktop. However, I can't find such a .zip file for Visual Studio.
Is there a way to install Visual Studio Community Edition without administrator rights?
Practically no. Visual Studio (Express and above, excluding VS Code) consists of multiple components that must be installed as admin, and will be required for the app you're debugging to be available as system-wide component. It might be possible to use ThinApp or its equivalent, but ThinApp can't even work with VS 2010 and it was by far the best of its class.
A (resource intensive) alternative to get VS on any PC will be packaging a VM with VS installed, either creating one yourself or get a ready-made ones. VirtuaBox is available as portable fork if you can't even get Hyper-V tools installed. But this still require kernel drivers installation, which means at least one-time admin access. Depending on your internet connection & budget, it might be more practical to setup a VPS with VS installed, then remote there.