Judge Ketanji Brown Jackson had a decision to make.

It was November 2013 and appearing in front of her waiting to be sentenced was Wesley Hawkins, a 19-year-old man who had pleaded guilty to downloading and trading scores of images and movies of child sexual abuse, including several showing boys who were under age 13.

The prosecution asked Judge Jackson to sentence Mr. Hawkins to two years in prison, arguing that his possession of the material was “extremely troubling and deserving of punishment.”

Mr. Hawkins’s lawyer was asking for a single day in prison. He contended that his client was young and remorseful and suffered from “emerging mental illness.”

In the end, Judge Jackson — then in her first year on the federal bench in Washington — gave Mr. Hawkins three months in prison followed by more than six years of supervised release.

In making her decision — “a truly difficult situation,” as she put it at the time — Judge Jackson issued a sentence lower than the ones recommended by both the probation office and the nonbinding federal guidelines. She also credited the defense’s claim that Mr. Hawkins should not be thought of as a pedophile because he was fairly close in age to the children depicted in the images he had.

While she acknowledged that Mr. Hawkins’s crimes were “serious” and “heinous,” she also said his case was not as troubling as others she had seen.

“I do not believe that you are similar in intent or as culpable as some of the depraved older adults,” she said.

The relatively lenient sentence was not unusual for cases involving images of child sexual abuse — especially for those of defendants who possessed such material but were not involved in making it. Nor was the decision out of line with comparable cases in the Federal District Court in Washington, where older defendants with larger collections of child sexual abuse imagery have not served prison time at all.

Still, the Hawkins case was thrust into the spotlight this week during Judge Jackson’s contentious confirmation hearings for the Supreme Court. Some Republican senators — chief among them Josh Hawley of Missouri — used the sentence in an effort to suggest Judge Jackson was soft on child predators.

In his pressing his attack, Mr. Hawley dug into the details of the Hawkins case, running through a disturbing tally of the sex acts, violence and abuse that was portrayed in what he claimed were more than 600 videos and images the authorities found on Mr. Hawkins’s computer. According to court papers, however, Mr. Hawkins downloaded 16 images and 17 videos, the latter of which were technically counted as 75 images each.

When Mr. Hawley asked Judge Jackson if the case reflected “a heinous or egregious” offense, she agreed with some exasperation that it did, but she also noted that judges consider many factors in deciding how long people should go to prison.

“Sentencing is a discretionary act of a judge, but it’s not a numbers game,” she said.

The line of questioning pursued by Mr. Hawley and other Republicans appeared to have some echoes of the QAnon conspiracy theory. Many of its followers believe baseless assertions that elites, including top Democrats, are child traffickers and pedophiles.

Andrew C. McCarthy, a conservative former federal prosecutor, defended Judge Jackson in an essay for National Review, saying that while he did not support her nomination, Mr. Hawley seemed to be misleadingly conflating “sex offenders,” who consume offensive imagery, with criminals who “prey on children” through acts of sexual violence.

The allegation that Judge Jackson had shown “an alarming pattern” of being soft on “sex offenders, especially those preying on children,” as Mr. Hawley put it, “appears meritless to the point of demagoguery,” Mr. McCarthy wrote.

According to ABC News, Mr. Hawley himself has voted to confirm at least three federal judges who also handed down sentences in cases involving images of child sexual abuse that were lighter than what the federal guidelines recommended. The guidelines are advisory, and as some Democrats on the Senate Judiciary Committee pointed out, federal judges considering cases involving child sexual abuse imagery often issue sentences far less severe than what the guidelines suggest.

The Hawkins case began in 2012 when Mr. Hawkins, who was then in high school, started downloading pornographic images from the internet and, according to his lawyer, felt “confusion and shock rather than arousal.”

A gay boy from a religious family that strongly disapproved of homosexuality, Mr. Hawkins was driven by a kind of curiosity about the images, according to his lawyer. His connection to the people in them seemed, his lawyer said, to be “one of identifying” rather than of “exploiting them sexually.”

Many of the images were, however, extremely disturbing, showing young boys engaged in a variety of sex acts, some of them violent. When Mr. Hawkins reposted some of the material onto YouTube, the authorities received a “cybertip” about him. A police detective posing as a fellow collector of images of child sexual abuse soon reached out to him by email and suggested they trade images.

Prosecutors say that Mr. Hawkins did eventually swap images with the undercover detective, sending some files and asking for others that he believed were of the detective’s 12-year-old daughter. When Mr. Hawkins was arrested in June 2013, prosecutors say, he was immediately cooperative and “took full responsibility for his actions.”

After he pleaded guilty that September, the case moved toward sentencing. In papers submitted to Judge Jackson, Mr. Hawkins’s lawyer, Jonathan Jeffress, argued that his client had indicated “no interest whatsoever” in the undercover detective’s repeated suggestions of a real-life sexual encounter.

Mr. Jeffress also submitted an evaluation by a psychologist claiming Mr. Hawkins did not “demonstrate sexual deviation” but was instead driven to watch the pornographic images as “a way for him to explore his curiosity about homosexual activity and connect with his emotional peers.”

Prosecutors, in their own filing to Judge Jackson, said they considered the psychologist’s report, and while they did not agree with everything in it, they acknowledged the report provided “useful insights” about Mr. Hawkins’s “personal circumstances, family situation and stage of development.”

Mr. Hawkins himself wrote Judge Jackson a brief letter saying how much he regretted what he had done.

“I have disappointed everyone in my family and everyone who has ever cared about me,” he wrote. “I hope that I can make up my mistakes and that this will not end my life before it starts. I swear that I will never do this again or any crime ever in my life.”

Both sides told Judge Jackson that prior cases supported their arguments.

The prosecution mentioned cases in which at least two men who got images of child sexual abuse from online chat rooms or from an undercover officer were sentenced to a full year in prison. The defense brought up cases of men who had larger collections of illicit material than Mr. Hawkins but did not serve prison time at all.

At the sentencing hearing in late 2013, everyone agreed that the case was challenging and reflected what a prosecutor called “very unique circumstances.”

Judge Jackson told Mr. Hawkins that the children in the pictures he possessed had been forced to commit “unspeakable acts” for “the gratification of sick people everywhere.” Some of them, she added, would never have a “normal adult relationship,” while others might turn to drugs or vices “to deal emotionally with the pain.”

But Judge Jackson noted that Mr. Hawkins never produced any pornographic material himself and that he had watched such material for less than a year. He was also young and remorseful and had the rest of his life ahead of him.

“It is tragic that you permitted your curiosity to jeopardize all of that,” she said.