“Everyone wants to read her mind,” said Chris Sagers, a Cleveland State University law professor and an antitrust scholar.

The conflict erupted after Epic Games introduced an in-app payment system within “Fortnite” that skirted Apple commissions and its policy requiring developers to use its own payment processing services. That prompted Apple to expel “Fortnite” from the App Store, provoking Epic’s antitrust lawsuit and its claims that Apple is exploiting the popularity of its devices to squeeze developers.

Apple says that it isn’t a monopoly and that competition is flourishing in a distribution landscape that includes Google Android software and gaming consoles. The trial, which kicked off last week, is expected to run through May.

Neither Apple nor “Fortnite” maker Epic are newcomers in Judge Gonzalez Rogers’s courtroom in Oakland, Calif.

In 2014, she presided over a lawsuit that accused Apple of suppressing competition for its iPod music players. A jury sided with Apple.

Apple later prevailed in another case before Judge Gonzalez Rogers. She declined to certify a class-action accusing Apple and

AT&T

of unlawfully preventing iPhone customers from switching carriers.

“She seems to keep ruling in favor of Apple,” said Prof. Sagers, but he and other scholars caution against reading too much into the earlier cases and rulings.

Judge Gonzalez Rogers has hinted in the past that she is willing to at least entertain an antitrust theory crucial to Epic’s legal argument: that a company can wield excessive power in the market for its own products and services, according to John Newman, a University of Miami antitrust law professor. Courts reviewing antitrust complaints seldom draw the boundaries of a market as narrowly as Epic is by claiming that Apple is illegally restraining trade within its own Apple ecosystem.

Just weeks ago, Judge Gonzalez Rogers was clued into the “Fortnite” craze while hearing a would-be class-action suit against Epic that ultimately settled.

At a 2019 hearing, a puzzled Judge Gonzalez Rogers asked the lawyers: “Is ‘Fortnite’ as big a deal as they’re saying it is?”

“My daughters think it’s kind of cool that I get to work for them,” Epic’s lawyer responded. Judge Gonzalez Rogers offered her own son as a rebuttal.

“He wanted to play videogames,” the 56-year-old judge said. “I told him ‘no’ so many times that out of paper, he created his own and he made little cards that he would put into the sleeve so he could play games. He’s now an aeronautical engineer, and I am quite happy that I said ‘no.’ ”

Raised in Texas, Judge Gonzalez Rogers attended Princeton University, working weekends cleaning houses and cutting grass to help pay tuition.

She earned her law degree from University of Texas, Austin School of Law and spent her early career as a litigator at Cooley LLP in San Francisco. In 2008, then-California Gov. Arnold Schwarzenegger appointed her to the Alameda County Superior Court. In 2011, then-President

Barack Obama

elevated her to the federal bench, with headquarters within an hour’s drive of Apple, Google,

Facebook

and

Twitter.

Her docket is tech-heavy but varied. Last year she made headlines with a sharply worded decision vacating a Trump administration rollback of an Obama-era climate regulation. Early on, she held that

Abercrombie & Fitch

ANF 1.26%

unlawfully discriminated against a Muslim employee by requiring her to remove her head scarf. The teen-apparel retailer said its dress code was essential to its brand image but agreed to change its “look policy” after the ruling.

Some of her rulings have been overturned on appeal.

The Ninth U.S. Circuit Court of Appeals overruled her decision to grant home detention to a man accused of trying to sell a grenade launcher to an undercover federal agent. Judge Gonzalez Rogers had allowed him to stay with his grandmother with a requirement that he spend at least an hour and a half a day doing book reports on stories of people who overcame difficult circumstances.

Along the way, Judge Gonzalez Rogers has gained a reputation among litigators as a jurist not to be trifled with. She has scolded litigators for gesticulations and facial expressions she found disrespectful, according to court transcripts.

In 2018, a corporate lawyer asked to extend a filing deadline. His excuse was a scheduled ankle surgery. The judge was less than sympathetic. “If you don’t like my schedule, go to a magistrate judge,” she said. “They will be a lot nicer to you than I will.”

Others have seen a warmer side. Though not approving of lunch breaks, she is a believer in snacks, feeding jurors chocolate-chip cookie-dough muffins baked by her son, muffins made by her mother and treats from Trader Joe’s.

“She takes a sincere and not-so-stuffy interest in the law, but it’s incredibly human,” said Thomas P. Brown, an antitrust lawyer at Paul Hastings LLP in San Francisco.

In the Epic v. Apple trial, Judge Gonzalez Rogers has shown a willingness to jump into questioning witnesses and had several sharp ones for Epic Chief Executive

Tim Sweeney.

In one exchange, she had dismissed Mr. Sweeney only to stop as she changed her mind with one more question about what he would do if he lost the case: “What is your backup plan?”

Mr. Sweeney seemed unprepared. “If Apple’s actions are lawful, then I acknowledge Apple would have the right to remove Epic from the developer program for any reason or no reason, and then it would be up to Apple to decide,” he said.

Her stance on videogames may be evolving. She has noted that her daughter has a Nintendo Switch. At a hearing last year, a lawyer for Epic was trying to make the point that the iPhone was unique for its portability compared with videogame consoles, when she interrupted.

“You’re forgetting the Switch,” she said. “I went online yesterday, and, at least, in the Bay Area, you can’t get a Switch anywhere.”

Write to Jacob Gershman at jacob.gershman@wsj.com and Tim Higgins at Tim.Higgins@WSJ.com