After you purchased the new domain, make sure to set it up, you can do it at Home → Setup:
As soon as you purchased and set up a new domain name, it starts the activation process. It takes several hours, usually, activation is fully completed in about 2 hours, if not quicker.
If the domain doesn’t work after a few hours after registration, most likely it’s only a DNS cache. DNS records need some time for updating and might be cached with your web browser or with your Internet Service Provider. Flushing DNS Cache should help you see your website.
While your domain is activating, you can already: