As far as we can tell, Black Adam's producer has confirmed Atom Smasher's place in the DCU.

Hiram Garcia, producer of Black Adam, seems to affirm that Noah Centineo's Atom Smasher has a future in the DC Universe.

Without his mask, Noah Centineo stars as Atom Smasher in Black Adam.

Hiram Garcia, producer of Black Adam, appears to have confirmed Atom Smasher's future on DC Universe.
Several characters from DC Comics were introduced to the DCU in the debut episode of Black Adam on October 21.
Black Adam, aka Teth-Adam, played by Dwayne Johnson, was formally brought into the DC universe and given the title of the film when he attracted the notice of the Justice Society of America, a new superhero squad in the DCU (JSA).
Aldis Hodge's Hawkman, Pierce Brosnan's Doctor Fate, Quintette Swindell's Cyclone, and Michael Rosenbaum's Atom Smasher made up the squad (Noah Centineo).

Garcia recently posted a series of behind-the-scenes images from the set of the smash movie Black Adam to Instagram, including one of Centineo in his Atom Smasher suit on a staircase.
The caption appears to guarantee Atom Smasher's future in the DCU, with Garcia expressing excitement for spectators to learn more about the character.
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Although Garcia's post shouldn't be seen as official confirmation, it does seem to indicate that the Atom Smasher from the JSA will return to the DCU.
Given the ambiguity of the JSA's fate at the end of Black Adam, this is great news, but it does beg the issue of when and where fans could next see Garcia.
More plausible than a cameo in one of the known forthcoming DCU films like The Flash or Aquaman and the Lost Kingdom is a cameo in a Black Adam spinoff or sequel.

A sequel or spinoff to Black Adam has not been officially announced as of this writing, but the film certainly laid the groundwork for more than one.
The DCU might create a JSA spinoff in the form of a program or film now that the JSA has been presented, giving them a chance to not only better establish the team in the DCU but also to extend it and examine characters like Hawkman, Cyclops, and Atom Smasher.
Both Garcia and Johnson have spoken publicly about wanting to make a sequel to Black Adam, so there is reason to believe that a sequel may be greenlit even if a spinoff isn't.
If so, that's the most likely way we'll see Atom Smasher again.

The Atom Smasher might also make an appearance in a Suicide Squad sequel.
Though it hasn't been officially announced, it's possible that the remake directed by James Gunn may receive a sequel, especially since Gunn is now co-heading the renamed DC Studios and the first picture was a critical success.
After getting into some issues with Black Adam, Atom Smasher was imprisoned and enlisted into The Suicide Squad in the comics.
Given that Centineo's Atom Smasher is so young and playful in Black Adam, it's unclear whether the DCU would continue this storyline, but there's plenty of room for the DCU to work in Atom Smasher's return, whether in a sequel to The Suicide Squad, another Black Adam project, or something completely different.