The unidentified former soldier was shielded behind a wood-and-plastic partition, and his testimony about the events leading up to Corrie's death were relayed into the courtroom over a microphone.
"I wish I could see the whole human being," Cindy Corrie said before the testimony began, her voice shaking.
She and her husband, Craig, travelled from their home in Olympia, Washington, to hear his testimony.
Three witnesses were to testify on Thursday, but Al Jazeera's Sherine Tadros, reporting from Haifa, said that only one gave testimony as "at the last moment the judge said he didn't have time for three witnesses".
The military commander in charge of the unit that included the bulldozer on the day Corrie was killed will give evidence at a future date.
Corrie's family filed the private lawsuit against the state of Israel five years ago after an Israeli military investigation into the incident concluded that the soldier operating the bulldozers could not see Corrie and closed the case.
Both the bulldozer driver and the commander claimed that they were not aware of Corrie's presence, and that civilians aren't acknowledged in a war zone.
Reporting from outside Haifa district court, Tadros said that the driver who testified on Thursday "kept reiterating two main points. Firstly, that he was working within a command structure, that he had his orders from above, and secondly, that he really couldn't remember even the most basic of details to do with that incident".
She also said that the driver "couldn't even remember the time of day that Rachel was killed," which was very difficult for Corrie's parents to hear.
"I haven't heard one moment of remorse, and to me, that's one of the saddest things," said Cindy Corrie during a break in the proceedings.
She later told Al Jazeera that she was troubled by the "disregard" and "lack of reliability" of the driver's memory of the details of the day.
"If you've killed someone, you'd think you might remember if it was in the early afternoon or late in the day," said Cindy Corrie.
The Corries are suing the government for the symbolic amount of $1, saying that Corrie's "unlawful killing" denied her her "basic human rights".
They have also accused the government of "gross negligence".
Corrie was protesting against Israel's demolition of Palestinian homes in the town of Rafah, close to the border with Egypt, when she was killed.
Source: Al Jazeera and agencies