It depends on the country, I guess. In France, there are no ARs at the lowest levels, so you always start as a center referee. You can get designated for games at your level as a referee, or at some higher level games as an AR.
Depending on your ranking at the end of the season, you can get promoted or relegated, just like teams.
But, if you have a preference for being an AR (due to an advanced age or just... preference), you can choose the "AR track" and become a "specific AR". You get promoted or relegated in the AR rankings.
At the top national levels, ARs all belong to the AR track.
This is an example of how it goes in France, from the top national level (Ligue 1) to the last level (for my regional league and local league)
referee AR1 AR2 4th ref.
Ligue 1 : Federal 1 Referee | Federal 1 AR | Federal 1 AR | Federal 1-3 Referee
Ligue 2 : Federal 2 Referee | Federal 2 AR | Federal 2 AR | Federal 2-4 Referee
National: Federal 3 Referee | Federal 3 AR | Federal 3 AR
CFA (L4): Federal 4 Referee | Regional1 AR | Regional1 Referee
CFA2(L5): Federal 4 Referee | Regional1 AR | Regional2 Referee
Regional Level for my region
DH (L6): Reg. 1 Referee | Regional2 AR | Regional2-3 Referee
DHR (L7): Reg. 1-2 Referee | Regional2 AR | Regional3 Referee
PH (L8): Reg. 2-3 Referee | District1 AR | District1 Referee
PHR (L9): Reg. 3 Referee | District1 AR | District1-2 Referee
District Level in my district
Exc(L10): District1 Referee | District2 AR | District2-3 Referee
PEx(L11): District1 Referee | District2 AR | District3 Referee
1D-P1D(L12-13): District2 Referee, ARs are one guy from each team
2D-P2D-3D(L14-16) : District3 Referee, ARs are one guy from each team
You can see there is (theorically) one specific AR per games. This one is in charge of the benches' side. The other one replaces the referee in case of an injury.
In Ligue 1 and Ligue 2, the ref is replaced (if needed) by the 4th official. But there are two specific ARs in National (Level3) and no 4th official : thus, Federal ARs must have been Regional 1 referees for 2 years before turning into specific ARs.