If you’re focusing on the CORE, you don’t need the SDK. However, when working on modules having the SDK is helpful. While you could manually copy the generated OMOD file to test your changes, it can be tedious.
Your issue might not be related to the SDK at all; it could be a connection issue. This could be due to the NPM proxy settings. Try removing them with the following commands:
$ npm config rm proxy
$ npm config rm https-proxy
If your internet connection is unstable, increasing the timeout might also help.
I also faced an issue similar to you in the past but I can’t remember how I fixed it 