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Of American-English origin, the phrase to put a bomb under (a person or thing) means: to disrupt; to shake up; to rouse to action.

This phrase occurs, for example, in a review of Elvis (2022), a film by Baz Luhrmann, which chronicles the life of the U.S. rock-and-roll and pop singer Elvis Presley (1935-1977) under the management of Colonel Tom Parker (Andreas Cornelis van Kuijk – 1909-1997)—review by Paul Whitington, published in the Irish Independent (Dublin, County Dublin, Ireland) of Friday 24^th June 2022 [page 28, column 2]:

In 1955, he [i.e., the Colonel] is managing a touring carnival and representing country crooner Hank Snow when he hears a strange noise coming out of a record player. It’s Elvis singing That’s Alright Mama, the incendiary single that will shortly put a bomb under the music industry. While the country hacks around him grimace, Parker thinks this kid might have something, especially when he finds out that he’s not black, but white.

These are, in chronological order, the earliest occurrences of the phrase to put a bomb under (a person or thing) that I have found:

1-: From The Tucson Citizen (Tucson, Arizona, USA) of Saturday 20^th September 1902 [page 1, column 1]:

The St. Louis Prosecuting Attorney Says He Will Put a Bomb Under the Police Department
[…]

ST. LOUIS, Mo., Sept. 20.—Circuit Attorney Folk is much displeased by the efforts put forth by the police and sheriff’s departments to apprehend Charles F. Kelly and the other missing delegates under indictment for bribery. Mr. Folk expressed today for the first time his sense of indignation at the lukewarm support given the bribery investigation by the constabulary. He intimated that unless the missing delegates be apprehended without further unnecessary delay, he would reveal certain facts which the police department would not relish being made public.

2-: From The Daily Oklahoman (Oklahoma City, Oklahoma, USA) of Thursday 14^th January 1904 [page 2, column 3]:

FLYNN FOR SEAY
SAYS THE EX-GOVERNOR IS THE MAN FOR REPUBLICAN NATIONAL CIMMITTEEMAN [sic].
LAYS CADE ON THE SHELF
Shawnee Man Has Been Groomed By the McGuire Faction For the Place—Seay Would Take It.

In an interview given out in El Reno, ex-Congressman Dennis T. Flynn announces himself for ex-Governor Andrew J. Seay of Kingfisher for republican national committeeman to succeed the present incumbent, Territorial Secretary Bill Grimes, and also says that Seay will accept the place. Mr. Flynn in this statement puts a dynamite bomb under the boom, organized by the McGuire gang, for Cash Cade of Shawnee, the territorial committee’s chairman, for the coveted place of national committeeman.

3-: From The Glasco Sun (Glasco, Kansas, USA) of Friday 11^th November 1904 [page 3, column 4]:

The war situation over in the far east seems to have settled into that condition which pervaded the political situation here before election. Somebody should put a bomb under it and start things going.

4-: From the baseball news published in The Kentucky Post (Covington, Kentucky, USA) of Tuesday 28^th February 1905 [page 6, column 1]:

SHADOW OF DOUBT ON LYNN RED BOOKING

One of Frank Bancroft’s February bookings will probably be sponged off the Red slate unless the minors put a bomb under the national agreement and blow it up. Frank Leonard’s Lynns are independents, and that territory belongs to the New England League. Fred Lake will move his old team to that big shoe town, just out of Boston, and the Red date with Leonard Aug. 16 will probably bring a protest from Lake and a cancellation.

5-: From Iowa Press Comment, published in The Daily Nonpareil (Council Bluffs, Iowa, USA) of Thursday 2^nd November 1905 [page 4, column 6]—what this paragraph alludes to is unclear; the U.S. newspaper publisher and politician William Randolph Hearst (1863-1951) was then running for Mayor of New York City:

“Even some respectable gentlemen are beginning to concede that Hearst may know something and may not intend to put a bomb under the country when no one is watching,” says the Dubuque Telegraph.