Hey, @byakuyamon
Eunice here from Shopify, thanks for posting, and welcome to the Community!
Yes, there are apps that can help with this. But, before we continue, I just want to ensure you have your products set up to be sold when they're out of stock. When creating your product, under inventory, ensure Track Inventory is ticked. This is generally ticked by default. Underneath that checkbox, you'll see another option to Continue selling when out of stock. Once this is ticked, the product will be available for selling when out of stock.
With regards to apps, I, first of all, recommend checking out the app Estimated Shipping Date by Omega. With this app, you're able to set and show estimated shipping dates for specific products, collections, vendors, or the entire store. This app is $4.99 USD per month to use and comes with a 7-day free trial.
Another app worth checking out is Estimated Delivery Date Range by SetuBridge. Similarly, with this app, you're able to display the expected delivery date for specific products and collections. This app is $2.99 USD per month with no free trial included.
It's worth noting that these apps do not state whether the delivery message aligns with inventory automatically. Meaning that once your stock hits zero, you may have to manually change the delivery message within the app for that specific product. If this is important to you I recommend reaching out to the app developer directly to enquire. Their support contact details are located within the app listings linked above.
Alternatively, you could hire a Shopify Expert to create the desired feature especially for you and your store.
I love that you're selling/planning on selling out-of-stock products. Capturing pre-orders upfront, before investing in production, can be an invaluable approach to product validation. I recommend checking out this awesome blog by Shopify to learn how to build up more hype for your sold-out products.
I hope this helps! If you have any questions please feel free to thread those below.
