I put a lot of effort into trying to reduce this to level 6 but sadly we are 1 skill short of being capable of doing that.
Everybody gets access to 2 skills from their background, until a background offers a 3rd skill this means we require 16 from other sources.
Races: Changeling and Half-Elf both offer proficiency in 2 skills, while Human (Variant) allows for 1 (but has the advantage of a feat)
Feats: If you want all the skills at a low level then Skilled becomes a mandatory feat. For added Expertise (plus a skill proficiency) Prodigy is around now for Humans or Part-humans (like half elves).
Rogue - Starting as a Rogue allows 4 skills. ALWAYS start as Rogue, because it is the only class which loses a proficiency by multi-classing. (Bard and Ranger have 3 proficiencies but add 1 if you multi-class into them, Rogue adds 1 but has 4 hence the lost proficiency.) Scout Rogue adds 2 further skills.
Bard - Multi-classing adds 1 skill. Going Lore Bard at level 3 adds an additional 3 skills.
Ranger - Multi-classing adds 1 skill.
Cleric - Knowledge domain offers you 2 skills at 1st level.
Warlock - 2nd level Invocations offer you proficiency in 2 skills.
Generally speaking these are the combinations you will use to build that lower level skill master, other options add skills but at a much higher level:skill cost.
If you are building for not just skill proficiency, but Expertise as well, you would be looking at Lore Bard 10 Scout Rogue 6 Knowledge Cleric 1 as either a Human or Half-Elf (to gain the Prodigy feat). This would allow you Expertise in (Bard 3 and 10 each offer 2 expertise, Rogue 1 and 6 plus Scout all offer 2 each and Knowledge offers 2, plus 1 from the prodigy feat) so you have Expertise in 13 of the 18 skills.
Btw If you go Half-Elf Lore Bard 18 Rogue 1 Knowledge Cleric 1 you can gain Magical Secrets (18th) for any 2 9th level spells you fancy, plus cast 9th level spells while still being proficient in every skill (but only Expertise in 9 skills)