In the past I have used Matinee actors with movement tracks to make doors open and close as well as moving platforms; in the latest update of Unreal Matinee is not labeled as “Legacy”, I could not find information on why it was replaced nor what it was replaced with. In my blueprints I would usually setup a trigger volume to begin door opening and reverse the play when the player is no longer in range, unfortunately, right-clicking in the event graph does not let me reference the Matinee sequence, nor does it my trigger. All documentation I could find is from prior to V.10, they all still have Matinee integrated as a tool and it is possible to add it to the even graph by right-clicking while having the actor selected in the World Outliner.
To reference an actor you have to either expose a variable and set it using the editor or get it by using GetAllActorsOfClass or you have to send it to the Blueprint from outside. For example where the different actors are spawned.
However, in your case I would recommend exposing two variables; one for the triggervolume and one for the actor.
Then you can simply connect a timeline to the event Overlap Begin.
From the timeline you can set the door rotation to open it slowly. To do this, double click on the timeline and add a float track and set the values as you want. The update execution pin will fire once a frame and it will give you an updated value of the float track that you can directly use to create the rotator for the door.