The issue was fixed after a quick chat on the required configurations mentioned here19.
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At the moment the Social Sign-Up options appear below the Sign-Up rules. if they are quite long it means that people only see the Email and Password options for signing up. Please can you move the Social Sign-Up options to be above the Sign-Up rules? This would create a more user friendly experience.
Shivam, when you send the "email invitation", all the user need to do is to click on the link in the email and create a "password". The system ill skip the "insert email" section as the link only works for that email receiver. So, by default, they will be logged in with the same email address that they have received the invitation on.