>But if this is the case I have to plan the dates manually and give special privilages to the users for those date?
Your problem will be how to allow a user who obtained the app on one date (free) to obtain the same rights as someone who obtained the app on a later date (paid). The only way to do that is through an IAP. A common scenario, not unlike what you are trying to accomplish, is the conversion from a paid app to a freemium app. It goes like this:
App released in 2018, Version 1.1, for $3 with full functionality.
App released in 2019, Version 1.2, for free but with limited functionality. App can be upgraded through an IAP for $3 to full functionality. Version 1.2 checks the receipt to determine the original_application_version. If that is "1.1" it upgrades to full functionality without needing IAP.
You want to do something similar. You would need an IAP to upgrade and you would check the date of first launch to determine if a free upgrade is appropriate. But this will generate lots of complaints since the 'date of first launch' may not be the 'date of purchase'.