There are two possible reasons you have to set the triggers first. One of them you can fix with some file work. The other can only be fixed by replacing the set triggers.
There are two different kinds of set triggers. One of them that is commonly used on factory made guns is the Double Set,
Double Lever or Double Phase type.
There are "levers" or "blades' on top of each trigger. The front triggers blade pushes up on the sear arm when the trigger is pulled so it can fire the gun without first setting the rear trigger.
Then, there is the Double Set,
Single Lever or Single Phase type. This trigger does not have a "lever" or blade on top of the front trigger so it is impossible to use it to fire the gun when the trigger is not set.
These
Single lever triggers are also designed so that the rear lever is always pushing up on the lock sear arm unless it is first "set". That will make it impossible to set the lock to half cock or full cock when the trigger is not first set.
Pull the trigger assembly out of your gun and compare it with the picture above. If the front trigger does not have a blade on it, the trigger is a Double Set,
Single Lever type and the only way to fix your problem is to replace the trigger with a Double Set,
Double lever (phase) style trigger.
If your trigger is a Double Set,
Double Lever (phase) type, the reason your trigger has to be set first is because the trigger assembly is installed too deeply into the stock or, more likely, its because you haven't adjusted the height of the blades to match the location of the sear arm on your lock.
To adjust the blades, you will need to file the blades tops down so they won't push on the sear arm when they are left in the "unset" condition.
Some set triggers have an adjustment screw on the rear blades spring so you can reduce the amount of force the spring exerts. Doing this will lower the position of the rear triggers blade so it won't be pushing on your locks sear arm. This screw I'm talking about IS NOT the screw that is between the triggers. It is another screw that is located behind the rear trigger.
If your trigger has this screw, before you do any filing, try adjusting the screw to fix the problem.
If the adjustment screw doesn't do the job or, if it doesn't exist the only solution is to file the tops of the front and rear triggers blade down so it won't push on the lock sear arm.
I guess I should also mention, if the set triggers are installed a little too deeply into the stock, sometimes the problem can be fixed by adding a wood shim between the triggers and the stock. IMO, it only works if the set triggers depth needs just a slight adjustment because by shimming the triggers this way, they can end up hanging down, outside the bottom of the stock. IMO, that can look pretty crappy.