Deliver working website to customer in MVP technique.
This allows them to add content, whilst you keep adding features.
You can then keep adding features and improving.
How to meet a tight/moving deadline
MVP – Make the page work, add features over time, responsive, etc.
About page is a good place to start.
Go the homepage last.
Pay attention to headers and footers early on to ensure they look good as you work through the pages.
Speak to the client early about questions and issues.