Think the game broke somehow ngl, for me it no longer advances towards the next day in the story, it keeps repeating the message about the dinosaur emerging :( Day after day (in the game), just the same message
I did, yeah... All in one day, I check the dinosaur, get a note, show the dinosaur note to grandpa, find the boarded up entrance to the mines, get a note, show the mines note to grandpa, dig up fossils, identify them, then go to sleep. The next day the dinosaur message repeats
Edit: Wait, I think I found something. Will update if it works out
I played throught both versions (1.2 and 1.3) again just in case and I'm certain it works fine. If you're still stuck, I made a walkthrough you could use: https://cortok.itch.io/fossil-island/devlog/925167/walkthrough-guide
I just rewrote it so it's more clear. Hopefully it helps.