We believe that Newt may have been there at Hogwarts during Harry Potter and the Prisoner of Azkaban to possibly retrieve information or something else from Dumbledore or from Hogwarts after traveling in time using a Time Turner. During the events of the Fantastic Beasts series, Newt may have had to get something specific from the future, probably to defeat the dark wizard Grindelwald. Newt may have used a Time Turner and come to Hogwarts at that time, probably even have met an Older Dumbeldore and returned to his time. Interestingly, this may also be the reason that Dumbledore eventually thought of using the Time Turner to help Sirius and Buckbeak, something that may not have been an obvious choice for him otherwise. An even wilder and extremely "meta" theory would be that Newt came to retrieve and then place the Marauder's Map itself, something that didn't exist in the time of the Fantastic Beasts series. This would open very interesting possibilities and several new connections between the Harry Potter and the Fantastic Beasts storylines.