Building a caster who never rolls to hit

That's literally all spellcasters. It's really easy to avoid to-hit spells, the only exception is warlock with eldritch blasts

Cleric support is probably your best bet. Friendly spells don't roll to hit, and when you are being offensive clerics have a pair of save based cantrips that will cover almost everything you could come up against.

Sacred Flame is a Dex save for Radiant damage, and Toll the Dead is a Wis save for Necrotic damage. Very few enemies are good at both those saves or resistant to both those damage types.

Halflings get the Lucky racial feature, letting them reroll the first natural 1 for any given roll. You can also then get the Lucky feat, letting you reroll another 3 times per long rest.

The rest is just picking whatever caster class you like and choosing spells that force saves instead of attack rolls. There are too many to list here.

Edit: Since you're relying on your spell save DC, you're going to want to maximize your casting stat more urgently than usual. It's generally easier to beat an AC with an attack roll than it is to get an opponent to fail their save. A sorcerer's Heightened Spell metamagic is very useful for when you really want to make your spell stick.

Reliable Talent from the rogue features lets you treat any skill roll less than 10 as a 10, but that's not worth 11 levels in a class that relies on attack rolls for the sneak attack stuff.

Just use any caster with a bunch of spells that have spell saves I stead of to hits. Some good ones are dissonant whispers, shatter, and then the vicious mockery cantrip has low damage output, but interesting support capabilities.

If you play a bard and grab spells like healing word and cure wounds on top of these, you can run a very support oriented build while having good damage capabilities, and being decent at almost everything outside of combat.

Shouldn't be that hard, just focus on spells that use saving throws instead of attack rolls or that don't need a roll at all. Would include most AOE spells (fireball, lightning bolt, spirit guardians), buffs and debuffs (enlarge/reduce, shield, blindness/deafness) and CC (web, grease).

There is even decent cantrip options like acid splash or toll the dead instead of eldritch blast or firebolt.

Arcane Cleric. Magic Missile as a cleric spell

All full casters CAN, but Clerics are built for it. Sacred Flame is a dex save, Word of Radiance is a save, and Toll The Dead is a save too. On the Cleric spell list, level 1 only has Guiding Bolt and Inflict Wounds for attack rolls, and youvwere going to use those slots for Healing Word anyway. You lose out on Spiritual Weapon at level 2, and that's it. I cannot actually think of another Cleric spell with an attack roll.

Bard is the classic version of this due to having very few attack spells, but the are also able to use weapons so that might lead you back towards what you are avoiding

an evocation wizard would also work

people generally go with Firebolt for them but "Create Bonfire" actually uses the level 6 "Potent Cantrip" feature!

Divination Wizard. Now there's a good use for those middle-of-the-road portent rolls. You can use them to save other players who roll ones.

Halfling alone solves half your problems