While it may seem like a little of an overkill, adding a game instance is the proper way to do it.
Though the door design above is rather poor I my opinion. Definitely should a score variable be added, as SymCreations995 suggested. Additionally, the door should have a OnAttemptOpen event which is called every time the player tries opening it; this event will then check whether all prerequisites for opening the door are met: the prerequisite may just be score for now but in case the requirements change in a future version, it is easy to just change the event’s implementation right in the door. If you have the player check it, like above, this may lead to the player class becoming very complex and difficult to maintain. Also, having the player perform the check violates the single responsibility principle as it should only be handling player input (and therefore notifying the weapon to fire).
Ideally, you also add a target actor, or an actor component which marks its owning actor as target. Either way, the target should be notified when a projectile hits it and increase the score. In the approach of creating a target actor class, simply listen for an OnActorBeginOverlap or OnActorHit event, depending on who projectiles are set up to collide. In the approach of creating an actor component, you need to bind a callback function in C++ to the OnActorBeginOverlap or OnActorHit delegate object, again depending on how collisions are set up; it might be able to bind the parent actor’s overlap and hit events in a component in blueprints, too, though I am not sure how and hope somebody else will be able to answer that. By creating this target actor you take away the score updating responsibility from the player class. This way the player class will only have one responsibility: handling user input (which notifies a weapon to fire among other actions like walking, jumping, etc.). You could simply use the first person shooter template adding the door, and target classes.
By the way, you can find the single responsibility principle, which I used to justify my design, and four other very important ones right here.