"Time in the Round", a novelette by Fritz Leiber; first published in Galaxy Science Fiction, May 1957, available at the Internet Archive; reprinted in the 1958 hardcover anthology The Third Galaxy Reader edited by H L. Gold. The story is also available at Project Gutenberg.
The Butcher, the youngest of the three boys and the one who causes all the trouble in the Time Theater, is the one with political ambitions (though he doesn't expect to seize power "next week"):
The Butcher achieved a fearful frown. "When I'm World Director," he said slowly, "I'm going to have warfare again."
"You think so now," Hal told him. "We all do at your age."
The older boys are going to the Time Theater, accompanied by the Butcher, who won't be admitted because he's under five. Physical time travel is impossible, as Hal explains to the Butcher:
"You've never been inside the Time Theater—you're not old enough yet—so you just can't know anything about it or about the reasons why it's impossible," Hal replied with friendly factuality. "The Time Bubble is just a viewer. You can only look through it, and just into the past, at that. But you can't travel through it because you can't change the past. Time traveling is a lot of kid stuff."
"I don't care," the Butcher asserted obstinately. "I'm still going to have warfare when I'm World Director."
"They'll condition you out of the idea," Hal assured him.
"They will not. I won't let 'em."
"It doesn't matter what you think now," Hal said with finality. "You'll have an altogether different opinion when you're six."
But there is a minority theory that physical time travel might be possible in some circumstances, as the AI interpreter in the Time Theater explains, after the Butcher has gotten in by a ruse:
"I believe," the interpreter cut in smoothly, "that you're thinking of the theory that the Time Bubble operates by hyper-memory. Some scientists would have us believe that all memory is time traveling and that the basic location of the bubble is not space-time at all, but ever-present eternity. Some of them go so far as to state that it is only a mental inability that prevents the Time Bubble from being used for time traveling—just as it may be a similar disability that keeps a robot with the same or even more scopeful memories from being a real man or animal.
"It is because of this minority theory that under-age individuals and other beings with impulsive mentalities are barred from the Time Theater. But do not be alarmed. Even if the minority theory should prove true—and no evidence for it has ever appeared—there are automatically operating safeguards to protect the audience from any harmful consequences of time traveling (almost certainly impossible, remember) in either direction."
"Sissies!" was the Butcher's comment.
Today's show in the Time Theater is from "somewhere in Scandinavia around zero in the B.C.—A.D. time scale":
The interpreter continued: "The skin-clad men we are viewing in Time in the Round seem to be a group of warriors of the sort who lived by pillage and rapine. The hooded figure is a most unusual find. We believe it to be that of a sorcerer who pretended to control the forces of nature and see into the future."
The Butcher, with help from the ancient shaman, breaks the walls of the bubble:
"A viewing anomaly has occurred," the interpreter announced. "It may be necessary to collapse the Time Bubble for a short period."
In a frenzy, his ragged robes twisting like smoke, the sorcerer rushed at one of the warriors, pushing him backward so that in a moment he must cross-section.
"Attaboy!" the Butcher encouraged.
Then the warrior was standing outside the bubble, blinking toward the shadows, rain dripping from his beard and furs.
"Oh, boy!" the Butcher cheered in ecstasy.
"Butcher, now you've done it!" Hal said, aghast.
"I sure did," the Butcher agreed blandly, "but that old guy in the bubble helped me. Must take two to work it."