Glocks come ready to shoot brand new right out of the box and require NO break in. Usually and you are a case in point, the new to Glock trigger system shooter needs a break in on pulling the longer traveling trigger.
Practice at home like stated earlier without any ammo in or near your practice area. After ensuring the weapon is clear and safe, dry fire the gun by slowly pulling the trigger and aiming at something in a safe direction.
You have already noticed there is a bit of take up on the Glock trigger before it breaks and causes the gun to fire. Try pulling the trigger to the point that all the take up is gone and slowly release the pressure from there but don't let your finger come off the trigger. This will help you learn the travel/take up distance in the trigger. The point here is to NOT cause the gun to fire.
After you are used to how far the trigger goes, now try reaching that point and slowly; I mean very slowly, continue applying pressure to the trigger until it breaks/fires. As with any weapon, it should surprize you when it happens. Now practice this for a day or try to pull the trigger as hard as you can WITHOUT firing the gun. This can help you get to a point that you may know the pressure to apply to almost over come the springs and pressures in your trigger group to ready the weapon to fire.
All this will help you to see that it is you not the gun, causing the rounds to fly left and low. Greatest part is you can do this in the home and not burn ammo. Speed will come but accuaratcy has to come first they say.
We can never miss fast enough, to win!
The devil is in the details. The trigger is long because of the Trigger Safety and it has to be released to start the chain of events necessary to fire the gun. After the gun has fired and recoiled, blah, blah, blah, continue to hold the trigger to the rear. NOW release the trigger slowly until you feel it reset AND STOP releasing the trigger there. Now the gun is ready to fire again, without all that take up in the trigger.
Happy shooting, be safe!