One of my least favorite parts of Edge of the Empire was the combat system.
Weapons are Death Star deadly, and non-combat class Soak is often so low that it pales in comparison, not to mention the incredibly jump in pricing for purchasing armor. In such, throwing what seems to be an average threat at a party can send multiple PCs into critical quickly.
Based on your party composition, group the party against equally threatening opponents. If you have a Hired Gun Marauder, have an enemy that will lock them in close combat, whether that be a human or a creature. (Looking at you, Nexu)
The same can be said for a Bounty Hunter with a large gun. Give them something large to shoot their guns at, because that’s what they’re designed to do. However, the large thing should take more than one bullet to go down, if at all possible.
This should be the centerpiece of fights; a hulking centerpiece that takes a focus of fire before dropping. Giving them slightly higher defense with equal or slightly lower offense can bring your fights into the fun stages.
If you have several squishy PCs that sit in the back (Smuggler, Technician, Colonist) give them threats that match their respective lethality. I can’t tell you how many times a group of Rodians with coordinated blaster fire put me into the negatives.
Giving the middle/small enemies the same defensive stats as the team often helps, potentially bringing their soak down one or two points. This will show how deadly blaster fire really is without overwhelming those not built for combat.
Overall, my best advice is to instead emphasize the narrative aspects of the system heavily. Fill your fights with environment, and encourage your PCs to use Maneuvers to throw over barrels, create cover, dive behind X or trigger Y. Start a panic, hit a well-placed Gravsled to cause disarray, or quickly close the blast doors.
If players enjoy shooting things, give them things to shoot. Nobody enjoys getting shot, so give them ways to not get shot. Then force them to use those Destiny points, giving you future fodder. You’ll modify difficulty by presenting options, it is up to the PCs to take advantage.