At the base level, there are a lot of public resources available for Unreal developers. There’s the official Unreal documentation that covers most of the built-in functionality for the engine, and the tutorial archive that offers a variety of video seminars for people to watch and work through. There are also official message boards and stack exchange-type question-and-answer sites where programmers can search for previously-asked questions and solutions so they can untangle themselves. Most of the questions you would need are handled through these resources.
Beyond this, there are the occasional niche issues where you might need a direct answer from the engine developers themselves or even need to write your own system or plugin to solve a problem the engine doesn’t handle out of the box. You can post to the official message boards where the engine team will respond occasionally, but it isn’t super reliable - you’re at the mercy of the developers who happen to be spending some time reading the boards that day.
For some teams, there is some direct back-and-forth with the Epic engineers in specific areas like working through a high-priority bug in the engine itself as an example. It is possible for AAA studios to work more closely with Epic engineers to try out beta features that aren’t yet part of the released engine. Really big budget and/or high profile games that need more support can call in favors with Epic to get more access as needed. But generally speaking, to my understanding problem solving is primarily about working within the Unreal support community at large and less about working super closely with Epic directly.
Got a burning question you want answered?