As others have pointed out, Google could scoop up tons of riders in a heartbeat, by announcing a ride share platform publicly (which would get tons of news coverage) and by advertising the feature within Google Maps, Waze, etc.
Google only needs to put together a one-sided marketplace, where Uber/Lyft had to build a two-sided marketplace. And Google already has a connection to billions (at least hundreds of millions) of potential riders.
It would also need to invest in the vehicles and the technology and the maintenance and the garage to store them in and pay the insurance on the vehicles.
All this to try to compete with Uber (which isn't profitable) in a few areas where the legal, political and climate ("we have cars in Chicago but they only run from March 1st to November 1st") options are favorable.
The marketplace is not the biggest issue that Google would need to overcome.
Google only needs to put together a one-sided marketplace, where Uber/Lyft had to build a two-sided marketplace. And Google already has a connection to billions (at least hundreds of millions) of potential riders.