TL;DR: you want to be a human (variant) Divine Soul sorcerer.
To start with, let's figure out what magical defenses we are dealing with.
The level 1-3 wizard spells we are up against are as follows:
- illusory script
- arcane lock
- Nystul's magic aura
- glyph of warding
- Leomund's tiny hut
- magic circle
The sorcerers can't contribute anything unique to the defense, and the cleric is merely able to create different glyphs of warding which we can deal with anyway.
You are going to need access to detect magic and dispel magic at 5th level. This is your bread and butter for removing many of the defenses including the following:
- glyph of warding
- Leomund's tiny hut
...as such, we are going to be starting as either a bard, cleric, druid, sorcerer, or wizard.
One of the more vital skills the character will need is Investigation. Firstly this will help find mundane traps, but also it'll help with certain magical ones. Because Nystul's magical aura can disguise some of them, detect magic may not be sufficient for all defenses. This will be used to locate and avoid/dispel the following defenses:
The best way to have high Investigation is to use the enhance ability spell and have Expertise in Investigation. This can be achieved by bards, clerics, druids, and sorcerers. Bards gain Expertise as a class feature; the other classes will have to pick up the Prodigy feat from Xanathar's Guide to Everything.
Mundane locks and vaults are likely to be bypassed using thieves' tools, but since we are buckling in for dispel magic, we won't be able to get Expertise in thieves' tools (which requires being a rogue). Instead, we could use the knock spell to bypass tough locks that simple proficiency fails to surpass. The main downside of the knock spell, however, is that it makes a loud sound. As such, the silence spell is also vital to this technique.
Knock also bypasses the following magical defense:
The only classes that get both the silence and knock spell are bards and Divine Soul sorcerers (learning silence through Divine Magic giving access to the cleric spell list). Divine Soul sorcerers are the better of these options since they also get access to guidance earlier than a College of Lore bard to make our basic thieves' tools proficiency that much more potent. Thankfully, Divine Soul sorcerer subclass is also in Xanathar's Guide to Everything so we can choose it and still gain the Prodigy feat for Investigation.
The remaining defenses
Because we must be a Prodigy to gain Investigation Expertise, our character race is limited to human, half-elf, and half-orc. This means that magic circle can't keep us out, so the only remaining defense that we need to get past is illusory script (in cases where the item we are trying to steal is disguised by this spell).
The only way to defeat an illusory script (which can't be dispelled without ruining the original text) is to have truesight, but the true seeing spell isn't available until level 11. The only way to get access to truesight earlier is through employing a monster that has truesight (none of the possible summons are low enough CR to be gained earlier than the true seeing spell) or finding a gem of seeing (a rare magic item).
Since truesight is out of the question without that magic item, you are better off just waiting the 10 days just in case there is illusory script when stealing sensitive documents.
Putting all of this together, we get the following build:
We start as a level 1 human (variant) sorcerer of the Divine Soul Sorcerous Origin with the Prodigy feat and the following ability scores:
- 16 in Intelligence (for that high Investigation score)
- 14 in Dexterity (for using thieves' tools)
- 14 in Charisma (since this is your spellcasting ability score)
- 12 in Wisdom (since Perception is marginally important)
- 10 in Constitution (you don't want a negative modifier in Constitution with only a d6 hit die)
- 8 in Strength (this is your least important ability; you can always use enhance ability if you need to carry something heavy)
Our background can be anything that provides you with skills you think might be important (Stealth might be a safe bet just in case even though someone else is dealing with getting in and out). We get our essential proficiencies from the following sources:
- Perception from Skilled (Variant human trait)
- Investigation from Prodigy
- Thieves' Tools from Prodigy
At level 2, we get Flexible Casting, and at level 3 we get Metamagic. Metamagic is not super important (except perhaps the occasional Subtle Spell) for your heists, so we will typically use Flexible Casting to convert sorcery points into whatever spell slots will be required for the heist (based on whatever intel is gathered by the person in charge of that).
At level 4, it is best to increase Intelligence since Investigation is so important, but you can get away with increasing Charisma to improve your spellcasting if you want. And finally at level 5, we get the dispel magic we chose sorcerer for.
The following spells are important to the heists:
- guidance (from the cleric spell list)
- detect magic (to find magical defenses that aren't obstructed by Nystul's magic aura)
- enhance ability (for Fox's Cunning usually, but also useful for Bull's Strength with heavy loot)
- knock (to open locks that we can't get through with thieves' tools)
- silence (from the cleric spell list to keep knock from alerting anyone)
- dispel magic (to bypass the more difficult defenses)
There are some additional spells that could be beneficial:
- absorb elements (in case a glyph of warding with Explosive Runes is not detected; is found in XGtE so it fits in the +1 source)
- lesser restoration (from the cleric spell list, in case a glyph of warding with a Spell Glyph is not detected; can remove certain conditions)
- find traps (from the cleric spell list, although nondetection might make this useless)
And here's a spell we don't get that would be very useful (maybe you could ask your GM if your sorcerer could learn it anyway since it is a domain spell for some clerics):
- identify (would help identify exactly what spells are affecting an object instead of just giving an aura like with detect magic)
Level 6 is kind of up in the air. You could do a number of options, each with their own benefits:
- continue in sorcerer to get more sorcery points and spell slots to deal with better defended marks,
- Multiclass as a rogue to get Expertise in thieves' tools
- Multiclass as a wizard to gain a number of useful rituals like detect magic, identify, find familiar, and unseen servant1
1: Credit to smbailey for mentioning the breadth of rituals this offers
Addendum: Magical Disguises
Since magical disguises are a nonessential benefit, I thought I'd mention that this build can provide these too. It can learn disguise self and alter self as a sorcerer, and glyph of warding appears on the cleric spell list.
If we create a Spell Glyph of disguise self or alter self, any of our compatriots can wear a magical disguise.