The cave / boulder puzzle
Enter the cave from Scorched Dunes [3]. Use Rocket Boots across the missing pillars, then Dynamite on the rubble from inside. The boulder moves into the cave, freeing the gusher in [2]. Return there to reach the next room.
Other early gates
In Scorched Dunes [1], push the box right onto the button to open the gate. In Outer Scorched Dunes [2], a BUX pickup is behind rubble under the hill. Feel Fine is listed in Outer Scorched Dunes [3].
Where the route leads
The next major dungeon is Ancient Tomb, where Great Flocci grants the Bottled Ship. The Shovel is obtained later in the Red Sun Temple, so do not use it as the answer to these first desert gates.