This is my first time GM'ing in awhile and honestly I've never felt like I was very good at the non-combat aspects of it. On top of this my players are not very experienced with the role playing aspects of the game.

4 of the 5 characters that will be in the party have already been created.

So far we have:

Rodian - Smuggler - Pilot

Wookie - Colonist - Scholar

Bothan - Bounty Hunter - Assassin

Human - Colonist - Doctor

I guess my biggest far is making sure I include everyone and give everyone chances to shine, But I'm already wondering how a Wookie Scholar is going to excel in an adventure such as the Trouble Brewing that is found in the back of the rule book.

I really don't want it to end up being the Bounty Hunter shines while everyone else just kind of follows along as he shoots everything (he upped his agi to 4, and spent all of his starting money on a single weapon)

What small ways can a Pilot, Scholar, Doctor contribute to the standard pre-made adventures? (trouble brewing, under a black sun)

Pilot: Trouble Brewing has a space combat scene. Under a Black Sun starts with a speeder chase through the city but not much after that. Good pilots often have high agility so he'll be handy with a blaster in most combats. Look at his other stats and skills, however. Did he put some points in Deception? He might be able to cheat at a game of sabacc. Charm? He should chat up any cantina owners or bartenders for information.

Scholar: Need a computer terminal sliced? Let the smarty-pants Wookie do it. Best of all, if he fails, he can just put his fists through the computer screen! If you do the duracrete slug optional encounter in UaBS, encourage him to make a Knowledge - Xenology check to give the party a bonus vs. the monster's armor as mentioned in the statblock. You don't have a mechanic so the scholar, with his high intelligence, is probably going to be patching up the ship.

Doctor: Need I state the obvious? Ol' sawbones there will patch everyone up after battle (and maybe during). High intelligence likely means he's helping out with ship repairs as well. The doctor in our campaign also assists the party face in negotiations and whatnot thanks to her high Presence. Re-read what I wrote for the Pilot or Scholar since some of those tips could apply here.

What ways can any character contribute in Edge of the Empire? Simply put: With anything! They can kick tables over to provide cover. They can help with Brawl check and try to grab an enemy's legs and maybe pin him down while someone else blaster whips him in the face. They can shoot a blaster. They can shoot a blaster, miss, but generate Advantage which they spend to describe how the missed shot hits a computer panel on the wall sending sparks flying, temporarily blinding one enemy and adding a setback die to his next attack. Even failure can be awesome in this game.

It's been a while since I've read any of those adventures, but in general, any group not looking to start a fight everywhere they go, will generally be creative enough to find alternate courses. And given the skillset of the group so far, I'd imagine the group isn't really set well for dealing with a lot of fights, even ones that are scaled-back.

For the pilot there's typically chases/ship combat in FFG adventures, and if you wanted to throw challenges in to make him stand out - maybe with some clever planning, he can take out all the enemy fighters by dodging and weaving through some obstacles. The Scholar and Doctor could be stepping on each others toes a little bit depending on how they're statted and played. But it's likely at least one of them will be more of a face character, and the ability to deal with people well already makes a player shine - especially if they can talk people down from a fight or into giving the group better deals. And then there's the knowledge skills each of the Scholar and Doctor will have - these can give insight on rough environments, give players who need to talk to NPCs insight on how to deal with people, or simply know where to go for certain things; knowledge skills are an incredibly great way to help players figure out where to go to next if they're at a loss.

In general, it likely won't be much of an issue for the other players to have their moment. But somebody only set up for fighting will generally be stuck being only useful for those occasions when fighting can't be avoided.

When it comes to combat, try putting pieces into the environment for the characters to interact with that they can use to help in.

The doctor or scholar can roll knowledge xenology to determine a particular chemical or mixture is poisonous to the particular species of the baddies. Together they can dive over the bar and mix up a bunch of alcahols together to come up with some poisonous to lob at the baddies.

If you want ideas for how brains can excel in combat situations, check out a few episodes of Doctor Who. How often does the doctor use a gun? And yet the entire universe is afraid of him.