Hi @ccleve and welcome to the Auth0 Community! We’re happy to have you 
I think we can get pretty close to this use-case, but let me try and break it down below.
This aspect may be tricky from an Auth0 perspective because at this point we have no idea who those users are. Something to possibly consider is maybe that ‘Enter your email to sign up’ message triggers a mechanism that calls the Management API and creates a User with a temporary password. Here’s some further documentation (not quite your use-case) but a number of the steps could be similar.
Alternatively, this part of the flow could simply be handled by your application which would still trigger an email event and the link supplied in the email would redirect you to your login page.
Depending on how you created the User, you could use our Universal login page to gather further information using additional fields for the user to fill out. Additionally here’s our resource on progressive profiling which may offer some ideas on collecting this data as well:
Depending on your implementation some of this could be handled with either Hooks or Rules to modify the user’s login flow (either by denying access to the app or whitelisting their entry).
Hope this information gets you a solid start in architecting out your use-case (apologies that the response is a bit broad).
Best,
Colin