Greene can handle the market share problem. Even though Google commands only 4 percent of the industry's revenue, based on data from Synergy Research Group, the pie is quickly growing. According to Gartner, the cloud infrastructure market will climb 31 percent a year to $61.9 billion in 2020, up from $16.3 billion in 2015.
In Greene's corner is an engineering juggernaut like none other, a company in parent Alphabet stuffed with $75 billion in cash, a $10 billion annual capital expenditure budget and a vast network of highly sophisticated data centers.
Open source projects, big data tools, analytics software and artificial intelligence projects are on full display across the sprawling Silicon Valley campus.
Greene likes to geek out on subjects like Kubernetes, Google's open-source container technology unveiled in 2014 to help developers scale, deploy and tweak their applications across machines and clouds. It's GCP's fastest growing product.
"Customers love that we're so committed to open source and open APIs," Greene said. Application program interfaces, or APIs, are a way for companies to let outside developers easily access their technology.
Read MoreWall Street's ongoing struggle to make sense of the cloud
Pushing back against Google's cloud momentum is a deep skepticism over whether a company that generates 90 percent of its revenue from placing ads in search results, YouTube videos and mobile apps, can win the hearts, minds and wallets of the enterprise.
Google, let's not forget, is built on giving stuff away to consumers in return for their personal data. Tracking users' whereabouts, behaviors and preferences enable the company to target you with relevant ads in search results and all over the web and establish deep pattern recognition to predict what you want based on how people with similar attributes act.
How can that very same company be trusted to lock down a corporation's most sensitive data — contracts, business relationships, intellectual property — so that its key assets are inaccessible to anyone, including Google?