You can get treasure maps by finding dead pirates that carry them. If you're near one (or if you've synchronised a nearby viewpoint, of course), it'll show up on your map as a treasure map. Interact with the dead pirate and you'll obtain the map.
There's no shovel needed for digging, you dig with your hands, so you only need to find a treasure map and travel to the indicated location. Treasure maps show a longitude and latitude location in the bottom right corner, and on the map is the location itself... X marks the spot.
Actual first place you can get this trophy:
In sequence 1; you'll find a dead pirate with a treasure map on the beach where you rescue Stede Bonnet. I've misread the map earlier but when looking at the longitude and latitude of the map I found I actually returned to this part; the treasure is located very near. The map actually describes the beach you find the map on; just walk away from the beach and look for a cave with a bit of water in it. Way back into the cave you'll find the digging spot.
If you're already in Havana and you don't have your own ship yet:
In Havana, go to the Cathedral of Havana. It's a big church in the northern part of Havana with a viewpoint on its southeast tower. It's west of the big red square (the forbidden area that is Castillo San Savador de la Punta) on your map, if you haven't synchronised viewpoints yet.
Just north of the Cathedral's north wall, in the bushes, you'll find a dead pirate - as stated above, it'll turn op on your map as a treasure map if you get close enough or if you've already synchronised the viewpoint. Interact wih the body and you'll get a treasure map; the treasure itself is in Havana. To be exact, it's way south in Havana, next to the end of th city wall, on the beach. If you go there you'll notice a bent tree, behind it is the dig location (just look at the treasure map, it's very straightforward). Just dig there and the treasure and trophy are yours.