And, in the same vein: Jermaine Dupri was still a teen when the song he wrote became a #1 debut for younger teens in the ‘90s, with Kris Kross and “Jump”.
Lorde was a teenager when she wrote “Royals.” Billie Eilish hit #1 with “Bad Guy,” though in fairness I think her brother writes the songs a lot more than she does. So it can still happen.
As far as I can tell, Ciara wrote “Goodies” — and promptly had it hit #1, in the US and the UK, as her debut single — when she was just eighteen.
Pretty recently, Desiigner was a teen who hit #1 with his debut single Panda.
A Taste Of Honey had a #1 debut single with ‘Boogie Oogie Oogie’.
Strawberry Alarm Clock, with ‘Incense and Peppermints’.
Rose Royce managed it with the ‘70s-tastic “Car Wash”.
Barry Sadler, with the Ballad of the Green Berets.
Anita Ward, with “Ring My Bell”.
The Singing Nun, with “Dominique”.
If there ever was a one hit wonder, then this! It was one of my favorite songs when I was four years old.
Heh. For me, I guess it would’ve been the #1 debut that was 96 Tears.
But a number of those sales were obstensively 45 rpm singles for Starship’s “Nothing’s Gonna Stop Us Now”. Gullible pre-teens put the 7" disk on their turntables and were surprised to hear Rick Astley’s hit blasting out of their speakers.
As a result, the total sales for Never Gonna Give You Up are often published with a footnote… or a shrug emoji.
Possibly that calls for the strains of Daniel Powter’s #1 debut, Bad Day. 
Quite a few novelty songs from the 50s and 60s met the criteria - most were one-hit wonders. Examples from “Billboard”:
David Seville: “Witch Doctor”. He later re-christened his voice as “The Chipmunks”, which reached number 1 with their debut song “The Chipmunk Song”.
Sheb Woolley: “The Purple People Eater”.
Hollywood Argyles: “Alley-Oop”.
Brian Hyland: “Itsy-Bitsy … Bikini”. He had several later hits.
Larry Verne: “Mr. Custer”.
From “Cashbox”:
Napoleon XIV: “They’re Coming to Take me Away…” (#3 on Billboard).
To clear up the “Love Me Do” thread:
It was released in North America on February 18, 1963 - but only on Capitol of Canada. It may have been hard to get in the US. It wasn’t released on a US label until April 27, 1964.
“Please Please Me” was released in the US (their first US single) on February 25, 1963 (Vee-Jay), and in Canada on April 1, 1963 (Capitol).
Another one folks can maybe bicker over: “West End Girls” was the first single from the Pet Shop Boys, who hit #1 with — well, “West End Girls”.
But, putting that aside: “Hooked On A Feeling”. No, not the single from BJ Thomas; the ‘ooga chaka’ version that was Blue Swede’s #1 debut.
Also interesting that it was the very first release on that record label, Red Bird Records.
That feat was accomplished again with Apple Records first release, the Beatles’ “Hey Jude,” in 1968.
For the flip side of another coin: How Do You Talk To An Angel ‘was the theme for the TV series The Heights. The single was released with Jamie Walters as lead singer, and it hit number one on the Billboard Hot 100 on November 14, 1992, but the series was canceled exactly one week after the song fell from its number one position.’
The Bellamy Brothers had a #1 debut single with Let Your Love Flow.