The Y-Wing presents a challenge because of the long flaps needed for the engines. Using a square to get the longest flaps means using opposite corners, leaving the folder with two very long flaps opposite each other for the body. Using the entire square ended up producing an unsatisfactorily thick model.
In the end, I simply divided the square in half into a right triangle. That provides the single point for the body and two for the engines/wings.
The result is recognizable but still inelegant. The body is still thick compared to the engines, and the shaping of the body makes it want to curl upward.
My next thought is to try a pair of rectangles, interlocked with a few locking folds into a T-shape. My default for rectangles is usually US Dollars. The linen material makes them easy to use for multiple doodles.