10 cups 1-inch pieces peeled watermelon
3 cups cold water, divided
1/3 cup fresh lime juice
1/4 cup (or more) sugar
1 1/2 tablespoons fresh ginger juice
If you cannot find ginger juice at the store, you can make ginger juice by peeling a 3-ounce piece of ginger and grate it over a plate. Wrap in cheesecloth; twist at both ends to squeeze out the juice.
Place 2 1/2 cups watermelon and 3/4 cup cold water in blender. Puree until smooth. Pour agua fresca into large pitcher. Repeat 3 more times with remaining watermelon and cold water. Add lime juice, 1/4 cup sugar, and ginger juice to pitcher and stir to blend. Add more sugar by tablespoonfuls, if desired. Refrigerate until well chilled, at least 3 hours. Serve in ice-filled glass. Garnish with lime wedge and serve.