You could start in the center and quilt the yellow blocks. Then move on the next color and quilt all the green squares in that section. Move on to the next color.
You could probably quilt the 4 corners in a diagonal method using coordinating thread.
Change thread colors with each color set of blocks (yellow, green, blue, etc.) and not the individual blocks.
Think about how you are going to move from square to square. Plan it out first and even draw on paper if you like.