Mailbox password changes, webmail access and sending/receiving e-mail via a mail client are all available as soon as your mailbox has been created.
However, it can take up to 30 minutes for our MX servers to accept new e-mail for your new mailbox. If you receive a “Mailbox does not exist” bounceback to a new mailbox within 30 minutes of it’s setup, this should be nothing to worry about and will resolve itself as soon as our MX configuration updates.