As Google rose to prominence, Microsoft became a bit of an obsession among executives. Every Monday as CEO, Mr. Page would hold all-day meetings with his direct reports, including Mr. Pichai, in which they would agonize, "How do we not become Microsoft?" recall two people present. They feared turning into a company that surrendered its dominance.

Mr. Pichai's approach has been to choose incremental advancements -- along with doubling down on Google's house products.

Around 2012, he clashed with Vic Gundotra, then head of social platform Google Plus, about rolling out messaging features to Apple's iPhone before Google's own products. Mr. Gundotra argued that Google's technology couldn't yet handle the feature. Mr. Pichai slapped the table in frustration, a person present says, and responded, "I don't even know what to say." He didn't want the feature out until it was ready across devices. Mr. Pichai prevailed.

One of his last major promotions before becoming CEO gave him oversight of Android, the mobile software arm. There, his major move was to clip the unit's ambition, two former employees say. He axed formal plans to make Android the dominant software across all of Google's products, reasoning that attempts to integrate them all would lead to internal conflict.

One upshot of decisions like that is that Google can sometimes appear a collection of loosely related fiefs, with its products more weakly integrated with one another than at Apple and elsewhere. In messaging, Google runs competing applications called Meet, Chat, Messages, Duo and Hangouts. The company has said it has no plans to combine them.

Mr. Pichai is uncomfortable delivering hard news. Tony Zingale, former chief executive of Jive Software, recalls Mr. Pichai's agita in 2014 when he told Mr. Zingale he would have to resign from Jive's board to devote himself to Google. Mr. Pichai appeared nervous and contrite, until Mr. Zingale told him all was forgiven. "You could just see him exhale," Mr. Zingale says.

"He agonizes over decisions. I've told him that before," says Twitter Inc. chairman Patrick Pichette, a former Google executive. "I don't think there are enough Rolaids in the world for Sundar."

In 2015, Google split itself into the conglomerate Alphabet. Mr. Page's first instinct was to remain chief executive of Alphabet and have no CEO of Google, but company advisers told him that was dubious under securities law, a person briefed says.

Instead, Messrs. Brin, Page and Schmidt retained control of the company's voting shares, giving them final say over company decision making. Mr. Pichai became CEO of Google, while Mr. Page led Alphabet.

Mr. Pichai beat out internal rivals including YouTube CEO Susan Wojcicki, who asked the company founders to let her report directly to Mr. Page. Mr. Pichai argued against it, and won.

Ms. Wojcicki said, in a statement through a spokesman: "I discussed YouTube having its own identity and culture to better serve our users, not being separate from Google."

Mr. Pichai for the first time visibly enjoyed the trappings of his role. He ordered an elaborate renovation of his executive suite to add an array of couches and more private space. A spokesman calls it a "collaboration area." Some at Google coined a different term for the new layout: Sundar's Palace.

As Google CEO, Mr. Pichai's purview now included all of Google's online advertising business, a colossus that takes up nearly a third of the $130 billion U.S. digital ad market and accounts for nearly all of the company's profits. This includes ads that run on Google's flagship search engine, as well as others that run on external websites but are placed by Google.

Again, Mr. Pichai took an incremental approach. Around the 2016 presidential election, Google's top advertising executives presented him with a proposal to end political advertising on search. They pointed out that political advertising amounted to minimal revenues, with a disproportionate headache.

Mr. Pichai overruled them, in part to avoid making political waves, people briefed say. Google continues to take political ads this election.

Firestorm

Mr. Pichai couldn't avoid politics in August 2017, when an internal memo kicked up a firestorm among the company's typically left-leaning workforce. In it, Google engineer James Damore suggested that men might be better suited for tech jobs than women.

Playing against type, Mr. Pichai moved quickly. Though some of his deputies urged him to let the incident boil over, he fired Mr. Damore within a week. The move made Google a renewed public enemy for conservative critics, and led to a lawsuit from Mr. Damore, later settled.

A willingness to bend to employee criticism soon damaged Mr. Pichai's relationship with one of his top deputies, Diane Greene, an Alphabet board member and head of Google's cloud computing division. Ms. Greene had discussed with Mr. Pichai the company's bidding to renew Project Maven, a Department of Defense project to better integrate artificial intelligence into its computer systems. When employees found out in 2018, however, thousands signed a petition objecting to the work.

Ms. Greene, believing she had Mr. Pichai's backing, defended the work, and was dismayed to be instructed to publicly reverse course due to the outcry. The incident helped force her departure from Google in early 2019, people briefed say.

John Giannandrea, now head of artificial intelligence at Apple, resigned from Google a few months earlier for similar reasons, the people say.

Several current executives say Mr. Pichai sees Google's role as a big tent, one whose products can improve the lives of its many users. In interviews set up at Mr. Pichai's request, several said that the chief executive had requested the company's artificial intelligence software, known as Google Assistant, work in languages other than English. He has pushed for the company's software to work on even its least expensive equipment.

In January, before coronavirus was international news, Mr. Pichai spent hours at home reading local media in Asia, and became convinced it would be a threat. The conglomerate was among the first major employers to send workers home in mid-March, and was the first major American corporation to extend the order to mid-2021. Mr. Pichai personally made the call, people briefed on it said.

He himself has continued to work in person at Google's Mountain View, Calif., headquarters, where the pressure facing the company is beginning to weigh on him, says longtime friend Caesar Sengupta, a Google vice president.

Some 13 years ago, the two split an office, where they played jokes on each other. One time, Mr. Pichai sent a fake resignation letter on behalf of an employee to Mr. Sengupta.

"The weight of the world is quite heavy on those shoulders," Mr. Sengupta says. "I haven't seen him prank anyone in many, many, many years."

--Liz Hoffman contributed to this article.

Write to Rob Copeland at rob.copeland@wsj.com