Nick here from Shopify. Great question!
I'm thinking your best bet here might be to check some of the apps from the Shopify app store which are focused around pre-orders. Let's take a look at some of the most popular ones below:
Because this feature is not native to the platform, an app or having something built custom for you would be your best bet for this. If you wanted to explore and investigate having something made custom for you, you could check out some of the Shopify experts from the Expert directory here.
Hopefully one of the apps can do what you need it to.
All the best, Nick