sniper rifle ?

If you start your character using an infiltrator or soldier profile, there will be a sniper rifle you can pick up near the shuttle when Cora tells you that there's ammo near the shuttle. Instead of just taking it, you should see an option to Equip it at the bottom of the interface (It's the Y button on the Xbox One). You'll need to decide which of the other two weapons (pistol or assault rifle) you want to replace with it. Sounds like you want to replace the Avenger, which will then go into your inventory. As a note, you can equip any gun you find as you're first picking it up in the field without going to a loadout station. After you've picked up the gun, however, you need to go to a loadout station to equip it.  If you start your character as a biotic, there will be a SMG by the shuttle rather than a sniper rifle.