If you are just signing in on your computer you can use BlueStacks to simulate an android phone. If it's asking for text verification setup a google voice number install the app in blue stacks. This will allow you to receive and send text messages and phone calls. Also you can install the Microsoft verification app via the google play store.
This will at least allow you to change the verification email to something else that you can use. Wouldn't do this on a public computer though.