Yes, this is possible if you sync your game data with cloud before deleting the app.

For more information on how to sync your data on cloud, please visit the following page.
https://support.eu.square-enix.com/faqarticle.php?id=16761&la=2&kid=77220&ret=faqtop&c=18&sc=0

*Please be sure to take this step before deleting the app. Otherwise, you will have to start the game from the beginning again.