Zardnaar
Legend
By level 3
I don't think there's any full caster that can keep up with damage focused Barbarians, Paladins, Rangers or Battlemaster Fighters in terms of single target damage. A warlock utilizing their super familiar might exceed them. A war cleric might could get close to them.
By level 5
Martials like Barbarians consistently can hit for 30+ DPR. Paladins should be similar. I don't think there's any caster that can do that kind of single target damage at that level.
That said, techniques like reaction moving with Spirit Guardians, upcast Moonbeam vs immobilized foes both give respectable single target damage while also being able to deal AOE damage. Though there is definitely a damage caster running out of gas issue at this level compared to the martials.
By level 7
Martials increase their DPR ever so slightly. Casters get access to additional techniques like upcast summon fey, coupled with their best at will cantrip/attack. There's alot more spell slot gas by this level and the previous techniques just work that much better in the higher level slots.
By level 9
Most martials haven't gotten very much additional offensive power by this point. I think at this point full casters tend to start outperforming martials at single target damage if they wish.
At level 11
Martials mostly have 1 last large push toward increasing their damage before extremely high levels. Casters are probably ever so slightly behind this for single target damage.
That said, good magic weapons, can really push things into martials favor throughout the whole level range.
And then there's also some of the 'questionable' spells/spell combos like CME+Scorching Ray (CME an obviously unbalanced spell0, or Magic Missile and Evocation Wizard's level 10 ability making the int damage bonus apply to all missiles (not a clear cut interpretation), etc.
Point being, there's going to be alot of variability in actual play when it comes to damage.
The other thing I'd suggest is that casters vs a single target, they don't really need to damage, they just need to use appropriate low level control spells. Couple that with good aoe damage/control abilities and casters are very good, even if martial single target damage might be a bit higher.
Level 3 best I've got is probably a warlock with hex+ Scorching ray nova strike and all 3 magic adept feats. They found local strike every encounter. Might not white room win but real game useful.
I suspect it's a sorcerer somewhere in the higher tier 2. But might be limited by fire damage hence sone combination of Scorching ray, Fireball, Chromatic Orb.