Something like Expiry, AdvancedPublisher or TimeRelease might help you. These stacks can hide or show parts of a webpage at specific dates / times. Either could be a good method to ‘soft launch’ a new website and then automatically have additional content begin displaying after certain dates.
In one of the websites I manage for a client, they often need to advertise trade events they are participating at and provide free tickets. We use the AdvancedPublisher stack to advertise forthcoming events and automatically delete the finished ones. Sometimes the ticket registration for certain events is only available 30 days beforehand, so we again use the AdvancedPublisher stack to alter the content / links shown when ticketing becomes available.
Count-down clocks and ‘website under construction’ messages are not considered good practice nowadays. Generally it is better to try and put as much content up as you have available and incentivise users to come back again.