on browser it is not possible. on mobile and PC it is automatic
if you see a "delete save data" button and you do not see a "resume old save" button, then saving should be enabled. try progressing 1 day and see if the game is saved.
if not, connect your device to a PC, navigate to this location, and see if the savedGame.json file exists here
Internal storage/Android/data/com.DefaultCompany.GravenousGlutton/files