Now, my RPG experience has been primarily through video games (this blog started as a pure World of Warcraft blog, and I'd say that's still its main focus) and one thing that video games have to contend with is that everything needs to be pre-programmed. As well-written as the characters in Mass Effect are (can't speak to Andromeda, which I have not played,) your interactions ultimately wind up being multiple-choice, and the game's not going to let you do anything the developers didn't anticipate.
My impulse in my campaign has been to push combat encounters with little fanfare - my general sense has been that if I send a monster at my party, there's going to be a fight. But I think that is a bit of a habit from video games.
Just because, for example, a goblin in D&D is chaotic evil, doesn't mean that it is necessarily going to kill everything it looks at.
So even though this is May, I'm going to make a kind of new year's resolution to open things up and encourage my party to deal with monsters in either non-combat ways, or at least more strategic ways.
I think one of the keys is allowing players to encounter monsters in contexts that don't necessitate immediate combat.
One idea (and I'm banking on the assumption that none of the players read this blog) is that I have a subregion of an area within my setting's equivalent of the Shadowfell (think more like the Dark World from Zelda: A Link to the Past) where there is a coven of Night Hags who control a town that used to belong to their mother, from whom they usurped the town.
My initial impulse would be to give the players a simple "kill their mother to get their help or kill them" choice, but I think the resolution here is to try to let the party surprise me. Anything from a Yojimbo-style playing-both-sides-against-each-other thing to providing family counseling to heal the rift between these evil fiends.
Only one of my players has played the game prior to this campaign, so I think I'll need to actively encourage them to try alternative approaches - not that going in guns-a-blazing isn't an option. I suppose that I could encourage this by A: having monsters that are not immediately hostile and B: sending them up against monsters that can wipe the floor with them, requiring them to try some other tack.