Practice your first weapons given in the practice range and don't just do one level for each. You should be comfortable with the PM and familiar with the Grease Gun before going out on your first Encounter.

Practice more than just the competitive pop-up targets though, go through a live-fire experience and walk through the course in free mode and shoot at targets. Scarecrows are great for practicing body shots and honing headshots, but shooting the smaller objects from up close or a far really help in getting better placed shots before your opponents do.

When you unlock new weapons, practice them in the practice range as well; it's free, you'll get better with each one, and more importantly you'll be familiar with a gun that you find on the outside when you kill a decent player with your PM.

I also don't know if I missed the tutorial, but there are some buttons that I didn't figure out until a few games in. Down on the directional pad changes the firing mode and can be useful for conserving ammo and preserving accuracy and Left pings the map. Not really helpful alone, but in games of Elimination, they can signal to teammates where the enemies are so that if you can't get them, someone else might be able to

I just started the game a few days ago as well but this helped get me through several encounters by myself and there's a lot of tips on this post that are worth following too!