Hey! Unfortunately completion stats are saved to your browser local storage, and if something goes wrong there (for example: running out of space due to data stored by other sites) there’s not anything I can do. Sorry to say it’s just one of the risks of using browser storage.
So restoring your times isn’t possible, but you can reveal puzzles you’ve already solved. Under About the Game -> Manage data, you can reveal all puzzles, or you can do it one by one with the Reveal Solution button. (Were you in the middle of the archives? Considering adding a bulk reveal to the archives if that would help in this kind of case.)