I see, thanks for providing additional context! One options would be to follow this guide for setting up an email invitation flow:
Otherwise, you can switch to the Classic Universal Login so that you have more configuration options. If using classic, you can use a query string parameter to the /authorize request to determine whether or not to display the sign up link.
Unfortunately, there isn’t currently a configuration option for the New Universal Login experience that would be able to show or not show the sign up link based on query params (related topic: Don't show "Sign Up" option on New Universal Login - #5 by dan.woda). You can also provide your use case in a feature request in our feedback category for the community and product team to review: Feedback - Auth0 Community