In her long-awaited first public appearance on Capitol Hill, Anne McGill Gorsuch, President Reagan's controversial nominee to head the Environmental Protection Agency, yesterday sought to reassure her critics by contending that she favored "workable compromises" and promising to be "non-confrontational" in her new job.

The environmentalists who strongly opposed her introduced an element of confrontation at the packed Senate Environmental Committee hearing, however. Their first salvo was from Elizabeth A. Davenport, coordinator of Environmental Action.

The nomination ought to be rejected because Gorsuch is "an administrative novice and lacks the necessary technical expertise" or background in conservation issues to run the complex agency and the complex laws it handles, Davenport said.

Witnesses from the Sierra Club, Friends of the Earth and the Environmental Policy Center joined Davenport in her view that Gorsuch's environmental background is "far from solid."

They argued that much environmental policy-making seems to have been taken over already by Interior Secretary James G. Watt and his Cabinet Council on Natural Resources and the Environment. They worried that Gorsuch would be no match for the Washington-savvy Watt.

The heretofore publicity-shy Gorsuch has been in Washington for some time, working out of an office at the Interior Department, not far from Watt. Yesterday she said she was chosen because of her training in "forging workable compromises" in the Colorado Legislature, and she promised she would work to do the same in Washington.

"EPA must be non-confrontational in its approach, leading by action and encouragement," she said. "I assure you that, it confirmed, this will be my guiding credo."

The Denver attorney, saying she had "actively sought" the nomination and was eager for the job, told a packed hearing room that she "had built a strong record of listening to all interested parties" while in the legislature. s"It is a record I intend to continue," she said.

Sen. Pete V. Domenici (R-N.M.) defended Gorsuch's experience as a Denver attorney and officeholder as parallel to, if not better than, that of the first EPA administrator, William Ruckelshaus, when he was named in 1970. "If Watt thinks he's going to be able to lead her [Gorsuch] around by the nose, he has another though coming." Domenici said.

Gorsuch, 38, agreed. She said she is confident that she will have full access to the ear of President Reagan and will report to him. "I don't feel bound by any vote anywhere," including votes of Watt's Cabinet council, she said.

Gorsuch spoke in a low, firm voice about her "deep-seated and longstanding concern for the environmental goals of the nation." However, she avoided making policy statements on several controversial issues surrounding the Clean Air Act, which is up for reauthorization this year.

Asked by Sen. Gary Hart (D-Colo.) whether she would recommend "fundamental changes" in the act to Reagan, Gorsuch said she found it difficult to be responsive. "There are better ways to meet the goals" of the act than the current law provides, she said, although she would "certainly not" change the clean air goals. Reagan's recommendations will be made before June 30, she promised.

Committee Chairman Sen. Robert T. Stafford (R-Vt.) expressed hope that the proposals could come in earlier so that work on the act could be completed this year.

Gorsuch appeared to change her position on another controversial question when Hart asked whether regulators should consider the cost of compliance to industry in setting primary health standards for the levels of pollutants that will be tolerated in the air.

At first she said she had reached no conclusion on the issue of the standards. The premise of the act is that the standards must protect the health of children, the elderly and ailing individuals.

Later, Domenici guided her to a different answer. "Presumptively the standard is correct if Congress sets it, isn't it? And you would not advocate changing that?" "No, I would not," Gorsuch said.

Hart also asked Gorsuch whether she approved of EPA's right to cut off federal aid to states that do not comply with environmental laws and EPA regulations. While a legislator she criticized EPA's threat to to that in Colorado over automobile emission control inspection plans, and was instrumental in forging a compromise that averted the problem.

"Do I think sanctions are the best way to go about the business? No, I do not," she said. "Incentives as opposed to sanctions are a far more effective tool."

But if incentives don't work, Hart pressed, what then? "I will give it a great deal of thought before I formulate my recommendations," she said.

Gorsuch said her commitment to regulatory reform at EPA "is not limited to withdrawal of unnecessary or overly burdensome singular regulations, but envisions a much broader scope involving the process by which new regulations are formulated and current regulations evaluated."

Sen. John H. Chafee (R-R.I.) said he was concerned that she "not be just a compromiser" but "a spokesman for the environment, for the Clean Air Act, for the Clean Water Act." He asked if that would "be truly your goal."

"Certainly," Gorsuch said.

Stafford, in a graceful statement on the role of the EPA in national life, cautioned Gorsuch that she would often "stand alone among other political appointees" and would "be accused of extremism, ignorance and incompetence" in exercising the obligations of the office "to speak for the nation's elderly and infirm to protect the air and water."

He said he was "confident that she possesses the qualities which this job demands" and would be confirmed easily, probably in a vote next week.