To migrate an existing site you'll want to create a second environment to work in:
- www.yourwebsite.com (your live site)
- new.yourwebsite.com (your new website)
Some of the other answers discuss setting up a second environment, so I'll leave that topic to them. For a large site, you have the good approach to not change many things. When your changing systems, when possible, it's often good to migrate things in a 1-to-1 manner. This helps keep things simpler with the migration and have more focus on the many other parts of the migration where you may run into complexity.
From your question, it sounds like the migration is driven by a redesign. While the design is an important part of the transition, there will also be several other phases of your migration and it's important to consider all of them to keep the site running smoothly and expectations aligned with an appropriate schedule.
Consider the following phases of the migration
- Planning - Determine who's responsible for what.
- Content Architecture - Build out the content model for the new site in Craft and create a mapping between all the sections and fields of the old site and new site.
- Template Migration - Migrate the HTML, CSS, JS to the new site
- Asset Migration - All of your assets will need to get into the new system. Even if you have your assets on a cloud service they will need to get synced with the new system and this can take time with large amounts of files. If your existing site manages assets in Rich Text fields or other messy-HTML type ways, consider what it will take to migrate those into your new data structure.
- SEO Migration - As you build out your content architecture and prepare for migration, you'll want to make sure you are taking SEO into account as you transition things over. Run a scan of your site before and after the transition to make sure you know if anything major changes. Make sure to setup 301 redirects and monitor your traffic for a reasonable period of time after the transition to confirm things are working as expected and tweak things.
- Data Migration - Migrating the data often takes several iterations to get right. If you have highly relational content, it may matter what order you migrate things in. You'll also need to coordinate this phase with the people adding content.
- Deployment - You can put a freeze on the main website and migrate and launch the new site. Or you can run a migration with most of the data and have people enter data into both systems for a week to confirm that things are working as needed with the new site. Either way, there will likely be some timing issues to sort out about the live site and the final data migration and the transition. It's much easier to plan to deploy the new site to a new server than to try to overwrite the existing site in the location where it is. Make sure you're considering SEO at this point and that you have a plan in place on how you are handling the transition and monitoring of your existing search standing.
In my experience with large migrations, there is ALWAYS something unexpected that presents a challenge. Don't expect to have an accurate estimate at the planning stage. Make sure people on your team understand that the estimate will be refined and get more accurate as you go through the phases of the migration.
If you are not familiar with parts of the migration process, consider hiring someone to help make sure parts of it go smoothly. It's better to spend the time up front getting things right or have a specialist help with a particular part you are less familiar with than accidentally lose all of your existing search listings.