The way I went: First get good at algorithms in some way. Then you join an unsexy infrastructure team at Google, there are tons of hard problems and potential for impact there. Then you use your accomplishments from the unsexy infrastructure team to join a sexy team, even at Google the kind of people who can actually improve the hard parts of Google are rare so that move isn't hard to make.

Some people directly join sexy teams, but that probably means they have some accomplishments from before, the hard part is getting a foot in that door and the unsexy infrastructure teams are a great place to start since there are tons of problems to solve there and not much competition for that kind of work. Most people just want to work with data models or publicly visible products, not the invisible services that moves millions of requests per second, but anything that moves millions of requests per second will be easy to have impact with.