Is there a link that
- opens the Microsoft Account login screen (where you can immediately start typing your email address), and
- after entering the password and answering whether you want to stay signed in, opens the Outlook webmail.
The link for that would be:
https://outlook.office365.com/mail/
This will open the Outlook webmail interface, and if not signed in it will ask you right on the page to sign in and then redirect you to the Outlook webmail interface.
Unsure if this will work for you as well but the below works on several machines for me for what you are asking.
Grab the link immediately after clicking the sign in button on this page