Short answer: No. DS cartridges use mask ROM (read-only) for game code and a small EEPROM/Flash chip for saves. When a game "deletes" a save slot, it overwrites that sector with zeros/FFs. There is no recycle bin, journaling filesystem, or wear-leveling controller to recover previous states.
.sav file to SD card, you can restore it.If the save is gone, treat it as a lesson: set up automated backups before the next playthrough.