Doctor Elizabeth Hammond is Trace's colleague at the New Mexico laboratory where Trace's accident occurs in the game's opening cutscene. Hammond and Trace are also somewhat close friends, as Hammond is the only one who sticks by Trace's side when he is outcast by other scientists.
In the first game, Doctor Hammond is depicted as a fairly young, androgynous white woman, probably in her 20s, with brown hair shaped into a bowl-cut. She is most often seen wearing a white labcoat and black pants.
Given that Dr. Hammond is the only associate close to Trace that we know of, it is highly likely that she accompanied Trace Prime on the first journey to Sudra. This is evidenced by the fact that Hammond worked closely with Trace on the theories needed to make Breach travel possible, and since Trace was still blind and crippled when he first arrived on Sudra, Trace would not have been able to make the trip alone, nor would he have been able to discover and utilize the Rebirth Chamber alone.
It can be logically assumed that Hammond and Trace comprise the "we" written in Faded Note (Note). At some point after, Hammond would make her way back to Earth, though whether Trace was with her or not is unknown.
In 2007, some years after her excursion to Sudra with Trace, she would utilize the research they'd performed together and create the first Ansibles- superluminal communication systems. At some point in the years following, she'd found Hammond Corp to manufacture and improve upon her earlier designs. And while her company grew to encompass other projects such as Jones Station in Antarctica, she privately continued the research on the Breach. As time passed, she came to agree with Trace about the implications of events that had occurred on Sudra, and the issues that could result from otherworldly technologies making their way to Earth.
Unfortunately, the bubble would soon burst and Hammond Corp would be facing severe difficulties financially. It's implied this would force Hammond into choosing to attempt an expedition to Sudra to find Trace (who had vanished in the intervening decades), or to continue upstream to find what had happened to A'ansur, the root world that had spawned her Earth. Her attempts at this would ultimately prove unsuccessful, and she would spend what remained of her life on Kiengir, ultimately opting to commit suicide after being cut off during an attack by drones ostensibly controlled by Lamassu.  Back on Earth, Hammond Corp would continue its fall, eventually being acquired by its rival Globe 3, and its CEO Indra Chaudhari.
However, as an exchange with Trace years earlier indicates, even her death may not have been her end.