From the noun nepotism, designating the showing of special favour or unfair preference to a relative in conferring a position, job, privilege, etc., the derogatory expression nepotism baby and its shortened form nepo baby designate a person whose career is believed to have been advanced by having a famous or successful relative.

The expression nepo baby occurs, for example, in the following, by Arwa Mahdawi, published in The Guardian (London and Manchester, England) of Wednesday 5^th June 2024:

Maya Hawke is honest about her privilege. Why are other nepo babies so defensive?
Congratulations to the actor Maya Hawke, who has just done something few of her peers seem capable of: acknowledge that one of the secrets of her success has been a little sprinkling of nepotism. The daughter of Ethan Hawke and Uma Thurman has always seemed to “wear her privilege with a shrug”, as a recent Guardian profile put it, but in a new interview with the Times, the Stranger Things star was even more frank about “not deserving” the life she has.

The earliest occurrences of the expression nepotism baby that I have found are as follows, in chronological order:

1-: From The Centralia Courier (Centralia, Missouri, USA) of Friday 17^th September 1915 [Vol. 25, No. 38, page 4, column 5]:

State Auditor Gordon ¹ certainly hung a “down and out” tag on ex-Gov. Hadley ² last Sunday. Herbert got a trifle gay and chided the Democrats for creating so many offices, spending so much money and practicing nepotism. In a “pot-shot” reply the auditor showed that the salary raise of clerks was the work of the Hadley administration; that Herbert’s regime added $354,930.99 to the state pay roll, while the Major ³ administration, including the Public Service Commission, only added the sum of $218,867.68. The auditor further showed that it was the Hadley’s administration that gave birth to the nepotism baby. Hadley had his father-in-law on the pay-roll, the State Game and Fish Commissioner put two of his own family on the pay roll; the State Beer Inspector found a good job for his hopeful son, and the Superintendent of Building and Loan Associations appointed his wife deputy under him. The Labor Commissioner gave a good birth to his son, and the Warden of the Penitentiary cared for his brother-in-law. The Republican Chief Justice of the Supreme Court put his son on the pay roll and the Superintendent of Public Schools found a place in his own office for his sister-in-law, from which the auditor opines that Hadley should not disown his own offspring. To a man up a tree it looks as if Gordon had put Hadley out of the running in the first round of the 1916 skirmish.

¹ John Pemberton Gordon (1866-1949, State Auditor of Missouri from 1909 to 1917.
² Herbert Spencer Hadley (1872-1927), Republican politician, Governor of Missouri from 1909 to 1913.
³ Elliott Woolfolk Major (1864-1949), Democratic politician, Governor of Missouri from 1913 to 1917.

2-: From Did I miss much?, by Steve Corbett, published in The Times Leader (Wilkes-Barre, Pennsylvania, USA) of Sunday 12^th January 1992 [page 3A, column 5]:

I was surprised to notice stretch marks on the Luzerne County Courthouse resulting from the painful birth of the new year’s first nepotism baby.
Judge Chester Muroski ⁴, shortly after being sworn in for another 10-year term, hired his wife, Cindy, as his law clerk to replace the one who resigned to take a job with the new D.A.

⁴ Chester B. Muroski (1939-2020), Judge at the Luzerne County Court of Common Pleas, Pennsylvania, from 1981 to 2009.

3-: From Phoebe Luckhurst’s Comment column, published in the Evening Standard (London, England) of Tuesday 1^st March 2022 [page 11, column 5]:

IF FURTHER distractions are required, may I offer the latest Gen Z outrage? On TikTok, the kids aren’t alright: they’re sharing their dismay that icons like Euphoria’s Maude Apatow, pictured, and model Kaia Gerber are so-called “nepotism babies”—in other words, the children of famous people. Apatow is the daughter of Hollywood producer Judd and actress Leslie Mann, and Gerber is an identikit version of her mother, Cindy Crawford.
Other “nepotism babies” include Lily Rose Depp and the Beckham sons.
While I wish celeb kids well, I agree with the spirit of the outrage—yes, it is annoying when the children of famous people find fame comes easily to them too. But may this wizened, disillusioned old bat of a millennial also say this to the kids? Guys, you have a lot to learn about the world.

The earliest occurrence of the shortened form nepo baby that I have found is from What Is a ‘Nepotism Baby’?, by Anna P. Kambhampaty and Danya Issawi, published in The New York Times (New York City, New York, USA) of Monday 2^nd May 2022:

For centuries, children born into rich, famous and otherwise powerful families have had a leg up in life, inheriting monarchies, business empires, wealth and star power. In some cases they’ve surpassed their parents’ status. This is what most parents wish for their children. It’s also often how power works, especially in Hollywood.
Now, a new generation is finding out that their favorite celebrities, talented as they may be, have benefited from a system that is not strictly meritocratic.
The phrase “nepotism baby” (or the diminutive “nepo baby”) has pervaded social media in earnest expressions of surprise (“just found out…”), envy (“pls god why couldn’t i have been a nepotism baby”) and even admiration (some favorites include Ms. Apatow, Zoë Kravitz and Dakota Johnson). Others are already talking about the next generation of nepotism babies, including the unborn child of Rihanna and ASAP Rocky (“a galactic nepotism legend already,” as one person put it).