When Google hired VMware co-founder Diane Greene to run its cloud business late last year, the company was clearly indicating that third place isn't good enough. Amazon.com and Microsoft have built sizable leads in cloud infrastructure, capturing billions of dollars that businesses are spending to offload their computing and storage needs. IBM is third, followed by Google. Greene, who ran VMware from 1998 to 2008, will talk publicly about her progress versus the competition on Wednesday at the Google Cloud Platform user conference in San Francisco. It's Greene's first major appearance since taking the helm. One not-so-subtle participant at the conference is Netflix, which just happens to be one of Amazon Web Services' marquee customers.

Google enters the event with momentum, after reportedly winning some business from Apple, another big AWS customer. (The company is also set to announce Wednesday that it won some of Home Depot's cloud business.) "This win helps Google Cloud Platform catch up to Amazon and Microsoft, at least in terms of perception, as a real third player in the space instead of a distant third," Evan Wilson, an analyst at Pacific Crest Securities, wrote in a March 16 report.

From a numbers standpoint, Google is actually a distant fourth in the $23 billion cloud infrastructure services market, according to Synergy Research Group. AWS ranks first with 31 percent, followed by Microsoft Azure at 9 percent, IBM at 7 percent and Google Cloud Platform at 4 percent, Synergy data show. That means of Google parent Alphabet's $75 billion in revenue, less than $1 billion came from cloud infrastructure. Gartner projects industry growth of greater than 30 percent annually through 2018 as more of the world's largest and data-heavy companies shift applications from their own data centers to the cloud to gain speed, efficiency and access across employees' devices.

Google faces a big challenge in finding its place in the market. Among start-ups and developers, AWS has set the standard. Its first product launched a decade ago and the service has become so transformative to the current generation of Internet companies that it's established a near-monopoly in venture capital portfolios. To show that it's not just for emerging businesses, AWS has signed deals with Pfizer, Comcast (parent company of CNBC) and even the CIA. Microsoft is the established name in the enterprise, having spent the past three-plus decades selling Windows software and servers and creating the world's biggest software business. Microsoft already has the sales force, client relationships and customer support systems in place, enabling it to sell to some companies that may be wary of Amazon's e-commerce roots. Read MoreMicrosoft cloud grows, but dwarfed by old stuff Google doesn't have enterprise support in its DNA or a lengthy history in the market. What it does have is a popular suite of cloud business apps like Gmail, word-processing documents, spreadsheets and calendars. "It's a huge asset," said Sacha Labourey, CEO of CloudBees, a developer of software that eases app deployment. "Creating a culture of enterprise sales and support is Diane's biggest challenge."

Google also knows how to build data centers as well as any modern-day Internet company. Just consider the technical sophistication required for processing over 1 trillion searches per year and billions of YouTube views a day. "We are able to take that infrastructure and computing power and optimize it for all customers," Google CEO Sundar Pichai said on the company's fourth-quarter earnings conference call. Pichai said that much of Google's increase in capital expenditures this year would be dedicated to bolstering computing capacity. The company has said it's adding cloud data centers in Oregon and Japan in 2016.