All the while, Google’s unique and freewheeling corporate culture appears to be crumbling. Activist employees have complained that Google is cracking down on workers who speak out on issues such as the company’s treatment of sexual harassment or working with the American military on technology that could be used to improve weapons.

Last year, Google fired several employees active in labor organizing for what it described as “clear and repeated violations of our data security policies.” It has also been working with a firm known for helping companies fend off unions.

Jack Poulson, a former research scientist who left Google in 2018, said the company’s focus on maintaining growth and keeping Wall Street happy had changed its character.

“The ethical lines are being rolled back,” said Mr. Poulson, now the executive director of Tech Inquiry, a nonprofit that helps tech workers raise ethical concerns about products they are working on. He said he had resigned from Google to protest the company’s efforts to introduce a search engine in China that would adhere to the Chinese government’s censorship requirements. (Google has said there are no current plans to launch its search engine in China.)

Google faces other challenges. Regulators and lawmakers around the world are scrutinizing the company for vacuuming up people’s private information and chilling the technology landscape with its market dominance. In the United States alone, it faces investigations from Congress, state attorneys general and the Department of Justice.

The company will also be under the spotlight this year with the American presidential election. It has grappled with criticism over how it allows politicians to target specific audiences with digital ads, a practice that it recently scaled back. The company is also scrambling to prevent misinformation spreading on YouTube and Google search results, as it did in the 2016 election.

These issues now fall on the shoulders of Mr. Pichai, 47, a former McKinsey management consultant who has proved adept at handling the traditional executive functions — like earnings conference calls with Wall Street analysts — that Mr. Page and Mr. Brin spurned. Yet he is often described as lacking the visionary chops of the company’s founders.