You could use a rhynio in modern ark to solo tame it, you can shoot off the back of a rhynio, and I believe a rhynio is faster than a quetz too. Or you could use the sap to send it to the ground. Point is, rhynios are a great thing to tame a quetz. i do recommend. You could also sap a quetzal to the ground and build a thatch box around it.