The Justice Department and dozens of states that brought the lawsuit argue that Google used the default deals as a “powerful strategic weapon” to block competitors and lock in its dominance in the search market.

No other deal has been as significant to the government’s case as a two-decades-long partnership between Google and Apple. The partnership has been worth $10 billion a year for Apple, which makes up more than 50 percent of the smartphone market in the United States, according to Counterpoint Research, a technology firm.

Mr. Cue’s testimony has been highly anticipated. While the case is focused on Google, the Justice Department has viewed Apple as a secondary player and the foremost example of how Google has used its deep pockets to maintain its power over the global search market. Should the judge rule in the government’s favor, it could cost Google and Apple billions of dollars.

The trial is the first monopolization case brought by the government in more than two decades, part of a crackdown on big tech by regulators appointed by President Biden. On Tuesday, the Federal Trade Commission filed a lawsuit against Amazon, accusing it of illegally protecting a monopoly over swaths of online retail by squeezing merchants and favoring its own services.

The Justice Department is also suing Google for illegally monopolizing the ad tech market. And the F.T.C. is suing Meta for using its dominance in social media to kill off competition.