If you want all the skills...
Half-elf (2 skills) background (2 skills, 2 tools) Rogue 1 (4 skills if you start rogue, thieves tools), knowledge cleric 1 (2 skills, 2 expertise), warlock 2 with beguiling influence (2 skills), lore bard 3 (1 skill for multiclassing, 1 instrument, 3 skills for lore bard)
level 7 = 16 skills, 4 expertise, thieves tools, 1 instrument, and 2 other tools. Not to mention plenty of cantrips.
And there's still the skilled feat as well.
10 Str, 14 Dex, 12 Con, 12 Int, 14 Wis, 16 Cha. Leaves you well rounded for all the skills. Or trade Str and Int for 14 Con.
Medium armor + shield, bless, eldrich blast, healing word, and cutting word to be competent ranged support in battle.
I would finish with bard 6, warlock 11, rogue 2, knowledge 1. With 20 Cha and inspiring leader. Though hard to say what order to go in.
Sorcerer 3 is also tempting for quickened bless.
The feat would add on 19 skills out of 18 choices. Why not go variant human and spend the bonus feat on skilled? That ends up with 18/18 skills and doesn't lose out on an ASI with a build that only allows for 3 ASI's (bard 4, warlock 4, warlock 8). I'd probably do the variant human as stated and then drop to rogue 1 taking warlock 12 for another ASI and invocation.
I consider it a novelty build anyway. Lore bards already have plenty of skill, jack of all trades, and peerless skill without all the hassle of multiclassing and the average bonus from peerless skill plus jack of all trades is higher than proficiency as well. Knowledge clerics with knowledge of ages can just add proficiency if needed to cover any skill or tool. Both are limited by BI dice or channel divinity but for how often it comes up as important I would call them better solutions to a desire for an all proficient skills style of character.
[MENTION=6802927]Inoeex[/MENTION], what you are describing sounds like you want lore bard 18 / warlock 2 and to spend the 2 invocations on agonizing blast and beguiling influence (maybe devil's sight). That's a ton of skills already with 3 from the class, 3 from the subclass, 2 from the background, 1 or 2 possible from race, and possibly 2 from the splash. That gives you more than enough to cover what is generally considered important and as I mentioned, jack of all trades half bonus still applies to the rest and peerless skill is available so it could already be in overkill territory.
That also keeps a person from delaying too much progression and only loses out on one ASI, and keeps all the magical secrets options plus progression is up to 9th level spells known. That's plenty of skill and spell support with eldritch blast for consistent damage. It's a common build. You might give up that last magical secrets for the 3rd level of warlock and use it for tome. More cantrips and more ritual access opens up options that won't cost spell slots but it's hard to say on that because it's giving up wish or other 9th level spells known as an options so depends on what you want from the character if you ever do get to those levels.