Number One with their first single

Ruby and the Romantics were an R&B singing group from Ohio. In 1963 they lucked out and got to sing “Our Day Will Come,” a fantastically beautiful ballad written by Mort Garson and Bob Hilliard.

The song went straight to Number One on the Billboard charts. Both the Hot 100 and the R&B charts, too. That was the group’s very first single.

And that’s amazing. How many famous artists have achieved that feat? I can’t think of any offhand.

This must have happened at some other time. I’m sure that some groups formed to record novelty records struck gold and were never heard from again, but those hardly count.

Do people have any more suggestions?

The Four Seasons started out with three #1s: “Sherry,” “Big Girls Don’t Cry,” and “Walk Like a Man.”

Near as I can tell, the first single from the Monkees (a) was “Last Train To Clarksville”, which (b) hit #1 — just like their second, “I’m A Believer”.

(Third one stalled out at #2.)

I feel like, going all the way back to Tin Pan Alley, with groups of people whose sole job is writing hit pop songs, it can’t be all that uncommon.
Quickly looking, Britney Spears and Christina Aguilera both did it. Mariah Carey’s first five singles went to number 1.

I think this would be a more difficult challenge if you restricted it to non-pop artists and/or singers or bands that write their own music (actually write it, not just a writing credit). Even then, Mariah may still be in the running.

I think if you look at a lot of artists that got very big, very very quickly, you’ll find many of them had #1 hits as their first single.
Don’t forget how easily these charts are manipulated…or not so much manipulated, but getting airtime on Top 40 stations doesn’t just happen. I don’t know how prominent it is today, but I recall a huge artist (Britney, maybe) talking about how payola really isn’t gone. No, the producers aren’t paying the DJs, but the radio stations have a deal that they’ll only play songs that come from a specific company and the producers pay those 3rd parties to push their records. A perfectly mediocre song can rise up the charts pretty quickly if every major city has at least one station that plays it a minimum of 12 times a day.

The Beatles’s “Love Me Do” was their first US single and went to #1 in the US. (This is if you don’t count “My Bonnie,” where they weren’t billed as the Beatles).

Little Eva hit #1 with her first single, “The Loco-Motion.”

I’m sure it’s been done several times by supergroups (i.e., groups formed by musicians who were already successful and well-known).

For example, The Highwaymen were a country supergroup, consisting of Johnny Cash, Waylon Jennings, Willie Nelson, and Kris Kristofferson. Their first single, “Highwayman,” hit #1 on the Billboard country chart in 1985, but all four of them had been performing for 2 or 3 decades at that point, and all already had numerous hits as solo artists.

Simon and Garfunkel (if you don’t count them as Tom and Jerry) with “The Sound of Silence.”
Lemon Pipers, “Green Tambourine.”
Archie Bell and the Drells, “Tighten Up.”
Jeannie C. Riley, “Ode to Billy Joe.”
Tommy James and the Shondells, “Hanky Panky.”
Steam, “Na Na, Hey Hey, Kiss Him Goodbye.”

It seems to happen a couple of times a year in the 60s.

The Spice Girls, with “Wannabe”.

They’re a good example of why this is harder than it looks. From Wikipedia.

Same goes for The Beatles.

It’s those non-charting singles that are hard to trace.

Or the barely charting ones. Everybody “knows” that the Doors’ first single was “Light My Fire.” It wasn’t. “Break on Through” was, though it didn’t make the Hot 100. And “California Dreaming” wasn’t the first Mamas and Papas single. That would be “Go Where You Wanna Go,” which didn’t chart at all. I learned a lot about obscure early singles when the internet came along.

Looks like Britney, Mariah, and The Monkees past that test, though. I hate “The Loco-Motion” and I’d classify it as a novelty song, but that’s probably just me.

“Fireflies” by Owl City

This reminded me of another artist I first heard on alternative radio in the US, in her case for several months to maybe even over a year before crossing over to pop (I think she was on her 3rd single at that point), Lorde with “Royals.”

Sylvia Fricker’s YOU WERE ON MY MIND by the We Five.

The Jackson 5 were the “first group to debut with four consecutive number one hits on the Billboard Hot 100 with the songs “I Want You Back”, “ABC”, “The Love You Save”, and “I’ll Be There”.”

“Old Town Road” is Lil Nas X’s first commercial release, and it’s the longest-running #1 in the history of the Hot 100.

Wasn’t that Bobbie Gentry? As far as I can tell, Riley’s first single — which hit #1 — was the one about how her mama socked it to The Harper Valley PTA.

Sheryl Crow, “All I Wanna Do,” topped a couple charts. It was actually her third single, but it was a single off her first album, that should count for something.

Lisa Loeb “Stay (I Missed You)”
Macklemore and Ryan Lewis “Thrift Shop”

Funkytown by Lipps Inc

But they didn’t remain famous very long, so kind of not what the OP meant.

Thrift Shop was the fourth single released from their debut album. Close but no cigar.

Stay is reasonably a debut single. There were some cassettes sold at shows and stuff, but no real release.

(I presume the choices for your post was inspired by the fact that these are the only two independent-label songs to ever reach Billboard #1.)

Yeah, but having a single from your debut album reach #1 isn’t exactly that uncommon. Paula Abdul’s debut, Forever your Girl, had four #1s (and an additional #3 when “The Way That You Love Me” was re-released in between “Cold Hearted” and “Opposites Attract.”) This is on the Billboard Hot 100, the usual yardstick for this. “All I Wanna Do” only made #2 on that chart, though it did top the US Adult Contemporary and US Mainstream Top 40 chart (which tracks radio airplay.)