Can customers log in using their order number?

[palettepaws]

Hi, I would like to know if there is another option other than the "Classic Customer Accounts" and "New Customer Accounts" Option. 

I would like to have something like this.
https://crownandpaw.com/
https://orders.crownandpaw.com/customers/sign_in

Letting the customers to login by using order number. Meaning that accounts will be created ONLY when the checkout is successful, and the registration process is NOT done manually by the customers.

Do let me know if there is a way to do it this way and customize and style the login page as well (couldn't find a way to customize like this on "Classic Customer Accounts" and "New Customer Accounts" Option). If there is a shopify App that can do this, do let me know.

Thank you for all the help in advance 😃