Albums that start on the Vocal.....

Cafe Tacvba - Avalancho de Exitos (Chilanga Banda)

British Sea Power’s Classic THE DECLINE of BRITISH SEA POWER starts with forty-one seconds of wordless sea-chanty harmonizing called “Men Together Today,” not sure if that is the right sense of Vocal for this thread.

Meryn Cadell - Angel Food for Thought (Secret)
Meryn Cadell - Bombazine (Jonny & Betty)

The Sugarcubes - Life's Too Good (Traitor, gotta turn up the volume)

About 4 or 5 Popol Vuh albums.

Let It Be

Suzanne Vega - Solitude Standing (Tom's Diner)
Miley Cyrus - Miley Cyrus & Her Dead Petz (Dooo It!)

Epic Soundtracks - Fallen Down (Rise Above)

In Visible Silence by Art of Noise starts with about a minute of looped vocal samples

Spacemen 3 - Recurring (Big City)

Todd Rundgren - Healing (Healer)

Todd Rundgren - Todd (How About a Little Fanfare?)

Moby - Play (Honey)

Caetano Veloso – the 1969 white album

Tigermilk (The State I’m In)

And The Boy With the Arab Strap

(The 2nd and 4th B&S longplayers also get damn close, but the feeblest of guitar strums are audible a matter of milliseconds before the voice.)

The Wedding Present, Watusi

Iron Maiden - Seventh Son of a Seventh Son

vampire weekend’s contra (“horchata”) and fotb (“hold you now”) both start with sharp intakes of breath and singing shortly after

“obvious bicycle” from mvotc starts right with the vocal. I thought “mansard roof” did too, but nope, keys come in first

Madness - One Step Beyond

Neko Case 'Wild Creatures' on 'The Worse Things Get....'. Albeit by only about half a second.

Soft Cell, 'Frustration' on 'Non-Stop Erotic Cabaret'.

Each of his first three albums!

Exactly what I thought of when I saw the title. I've used it in a music quiz to a friend before.

If we can have Let It Be we can surely have

We are the Night (distorted, alas)
GodWeenSatan
Revolver
Headquarters

?

if distorted vocals count, then:

Daft Punk - Homework (Daftendirekt)

The Piper at the Gates of Dawn

If we're counting vocal and music at the same time (as with the Play example) then The Wall

if spoken word counts, then:

Orbital - The Brown Album (Time Becomes)

age of chance : 1000 years of trouble.

'there's a beautiful noise coming up from the street ..

Not sure if this really counts because of the 20 seconds of noise before it but I love to see it mentioned

and on the vocal-and-music-at-the-same-time tip:

American Music Club - Engine (Big Night)

McCartney's Give My Regards to Broad Street opens with "No More Lonely Nights."

Spiritualized - Ladies and gentlemen we are floating in space (title track)

The Kinks - Sleepwalker (Life on the Road)

The Kinks - Something Else by The Kinks - (David Watts)

Carter USM - 3O Something (Surfin' U.S.M.)

Bodyswap was on TV recently but with most of Rimmer's speech removed. For shame.

The other Elvis's first album begins this way too ("Well it's-a one for the money"). So does Cliff Richard's studio debut Cliff Sings, with the same song.

Some others:
Gene Vincent and his Blue Caps - Bluejean Bop!
Little Richard - Here's Little Richard
Tommy Steele - The Duke Wore Jeans
Buddy Holly - That'll Be the Day
The Zombies - Begin Here
Little Richard - The Rill Thing
Bee Gees - 2 Years On
Elvis Presley - Elvis Now
The Beach Boys - 15 Big Ones
Paul McCartney - Flowers in the Dirt
The Divine Comedy - Fin de Siècle
Sparks - Hello Young Lovers
The Beach Boys - The Smile Sessions

age of chance : 1000 years of trouble.
'there's a beautiful noise coming up from the street ..

Not sure if this really counts because of the 20 seconds of noise before it but I love to see it mentioned

― you can see me from westbury white horse,

was wondering if i was going to get caught out.
i posted, then dug out the track and realised re the industrial noise starts before steven e appears.

Both With the Beatles and Beatles for Sale start on the vocal.

McCartney's Give My Regards to Broad Street opens with "No More Lonely Nights." ― The self-titled drags (Eazy)

I hate to be a pedant but the album version of "No More Lonely Nights" starts with some atmosphere and a bass riff.

I assume a capella and choral music (e.g., Gregorian chant) is disqualified?

Although, I was about to cite Enigma but it turns out that the MCMXC a.D. album started with a synthy bit. Alas.

The Holy Bible

If we're counting vocal and music at the same time

As “Help!” was listed in the OP, I assume we are…

indeed

wrens - seacaucus

I hate to be a pedant but the album version of "No More Lonely Nights" starts with some atmosphere and a bass riff.

Whoops, was assuming it started as the single version does!

Jean-Michel Jarre's Zoolook starts with a processed vocal noise. Not sure if that counts. Both Kevin Rowland's My Beauty and Propaganda's A Secret Wish start with dialogue. Probably not what the OP intended.

And of course Otomo Yoshihide's The Night Before the Death of the Sampling Virus, but that goes without saying.

Another in the speech pile: Portishead's Third

Shellac’s 1,000 Hurts, with its spoken audio calibration.

Laurie Anderson: Strange Angels (Strange Angels)

They say that heaven is like TV
A perfect little world that doesn't really need you

If we're counting vocal and music at the same time

Roxy Music, For Your Pleasure, (“Do The Strand”).

Two albums that start with vocoder:

Kate & Anna McGarrigle, Love Over and Over (Move Over Moon)
Tangerine Dream, Cyclone (Bent Cold Sidewalk)

Keyshia Cole's sophomore album JUST LIKE YOU. The song is "Let it Go". Technically there's a quick record scratch before she sings acapella, though.

latest Costello album also starts with the vocal (Farewell, Ok)

All Saints s/t

Aphrodite's Child, 666 (The System)

Hot Chip, Freakout/Release (“Down”)

Oneida - Each One Teach One

Arab Strap - Philophobia
"It was the biggest cock you'd ever seen..."

I opened the thread specifically to see if this one had been mentioned yet.

Nicely done, ILM.

Terence Trent D'Arby - Symphony or Damn (Welcome to my monasteryo)

Jeanne Balibar - Paramour (Le tour du monde)

Charli XCX - Crash (Crash)

Gun Club Miami Jeffrey Lee vocal gets joined by rest of band.

Does a cough count cos Junkyard starts with that before Nick sings about the death of his dad on Dead Joe.

Johnny Hates Jazz’s “I Don’t Want to be a Hero” sounds very very close to Shalamar’s “I Can Make You Feel Good”

Sorry - wrong thread! Argh!

Stevie Wonder - Hotter Than July

Badfinger "Ass" ("Apple of My Eye")

American Life

Songs About Fucking

Medúlla by Björk

https://en.wikipedia.org/wiki/Category:A_cappella_albums

Frazier Chorus - Sue

Big Audio Dynamite II: The Globe (Rush)