If we're talking about the classic idea of LEVEL, you'll always start on Level 1 not Level 0, if we're talking about points/score, you're always starting at zero.
So it ultimately depends on if the number in the scoreboard should reflect Level or score.
I'd have the player start on level 1 with the score 0.
Meaning your mode would display Level 1: Weaponname on the HUD but write a score of 0 in the scoreboard.