After you purchase a new domain, make sure to set it up, you can do it at Home → Setup:
As soon as it's done, the activation process will start. 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 due to 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: