If first time quetz taming use friend with a high stamina army and get your friend to pick you up and knock out the quetz however if it gets knocked out over the side of volcano or mountain it is 95% properly gonna die. Your best bet is to try and stay away from mountains and hostile areas eg. Ten base or giga den, and prepare for the slowest tame of your life if you don't have Rex kibble or prime meat.
The fun way is to jump off and grapple to your argie and whistle it to attack and since argies are slow it won’t catch up in time so tranq till it goes out also bring parachutes and consider liking so more people will know
If you drop a quetzal due to knockout, and it lands next to a giga...just know, the quetzal belong to the giga. Now you get to watch your would be quetzal get eaten by a giga. Now you can go home and cry.