Rogue 1 / Ranger 1 / Knowledge Cleric 2 / Bard 5;

By 1 you've got proficiency in 6 skills and expertise in 2
By 2 you've got proficiency in 9 skills and expertise in 2
By 4 you've got proficiency in 15 skills and expertise in 4
By 8 you've got proficiency in all skills and expertise in 8

Bard also means you've got Bardic Inspiration, by 9 (at the latest) that's an extra d8 4x per short rest when you need it.
Cleric also means you've got guidance at will for an extra d4

The order of these can be adjusted but post-respec you want Ranger before Bard so you can potentially use expertise on Ranger acquired skills.

Githyanki would of course accelerate getting to full proficiencies, and you could eliminate the Ranger level, but they're unattractive and ultimately Ranger is what gives your heavy armor proficiencies so I'm not convinced that it's universally "better" at the end of the day. In terms of a character which is Drow and Dark Urge origin, this is what I end up with, ignoring item boosts outside the headband of intellect:

Str (+0)
Athletics (+) (+4) (Rogue)

Dex (+4; Graceful Cloth gives +2, Base 16) (Advantage: Graceful Cloth)
Acrobatics (+) (+8) (Rogue)
Sleight of Hand (++) (+12) (Ranger) (Bard Expertise)
Stealth (++) (+12) (Rogue)

Int (+3; base 8, Headband of Intellect sets to 17)
Arcana (++) (+10) (Knowledge)
History (+) (+7) (Ranger)
Investigation (++) (+10) (Rogue)
Nature (+) (+7) (Ranger)
Religion (++) (+10) (Knowledge)

Wis (+2, base 14) (Universal Proficiency from Knowledge Cleric) (Advantage: Owls Wisdom)
Animal Handling (+6)
Insight (+6)
Medicine (+) (+6) (Dark Urge)
Perception (++) (+10) (Drow) (Bard Expertise)
Survival (+6)

Cha (+4; 2 Stat Gains from Events, base 16)
Deception (++) (+12) (Actor)
Intimidation (+) (+8) (Dark Urge)
Performance (++) (+12) (Actor)
Persuasion (+) (+8) (Bard)

Am I missing other sources of expertise or significant ways to improve skills? Can this be done better, setting aside accelerating getting to this point via alternate choices for Race or background?