Google partially withdrew from mainland China in 2010 and moved its servers to Hong Kong after a fallout with Chinese officialdom. Access to its services has been blocked or disrupted since shortly before June's 25th anniversary of the Tiananmen Square crackdown.
Wang Long, who describes himself as a "law worker", sued China Unicom over his lack of access to Google at the Futian People's Court in the southern boom town of Shenzhen, which neighbours Hong Kong.
The hearing took place on Thursday, a document on the city's official litigation service website showed.
On his account on China's Twitter-like Sina Weibo, Wang said that China Unicom's lawyer hesitated to answer when the judge asked whether Google's websites can normally be accessed.
Eventually, the advocate said that he was "not sure whether he can tell (the court) or not", sparking laughter from the gallery, Wang said.
He added that the judge ordered the clerk to record that the websites were not accessible, but it had nothing to do with China Unicom.
Court officials were not available to comment when contacted by AFP on Friday.
A ruling is expected to be made before October, the state-run Global Times newspaper reported.
It quoted Wang, 25, as saying that he had a contractual relationship with China Unicom. "They should offer me telecom services, yet they still failed to provide access. They should be held responsible for this failure," he said.
Wang has also sued China Mobile, another state-owned telecom carrier, and the court agreed last week to hear the case, another document on the Shenzhen website showed, without giving details.
The Global Times, which is close to the ruling Communist Party, quoted what it described as a "Beijing-based expert in cyber security, who requested anonymity" as saying Wang had sued the wrong opponent.
"It is Google that should be blamed, since it does not operate its business in China," the "expert" was cited as saying. "I call on companies like Google or Twitter or Facebook to offer services in China and accept [proper supervision]."