Unless you have a backup, it's probably not possible. What type of messages are these and what phone/android version are you using? Just in case there's a chance.
File recovery software from a computer is unlikely to help, since (a) since Android 4.0 the USB connection has used MTP rather than USB mass storage (so doesn't grant low-level access to the filesystem), (b) assuming you mean SMS the messages are not stored as separate files but as entries in a database in an area of storage that's not directly accessible without root, and (c) for any device shipped with Android 6 or later the internal storage is encrypted by default, so any file recovery software isn't going to be able to make sense of the data. Any utility running on android itself will need root access to do this, and even then I'm not confident. So as I say I strongly suspect you are out of luck.