Of course! The short answer is, "start with a little bit of spending cash"!
You can use the exact same steps I start my Brute with on Day 1. Head to the START Vendor, pick up some Amplifiers (1k a piece at level 1) to give you an overall stat buff, grab Plasmatic Tasers and Hand Grenades for AoE, and use the Prestige Enhancements in your ST attacks for bigger targets!
There isn't really a point to turning on bosses if they're just acting as giant road blocks as you clear maps. All you're doing is decreasing your xp gain overtime, so don't feel bad for leaving them off until you have a bit more power!
Another piece of advice I give in the playthrough is to leverage damage procs over damage aspect as you level. In your early career, enhancement aspect doesn't contribute much to your overall output as much as adding another solid number to your damage will. You can see me use these to great effect with the Brute, effectively tripling my damage with the little amount of slots I have available during the lower levels!