They want the commission to go back to the drawing board.
But the commission said it would rigorously defend itself, and denied its advice was not ambitious enough.
It said the lawyers' call for steep cuts before 2030 had no regard for the impact to society, and that the commission's plan met the country's net-zero objective.
NZ a large per-capita emitter
Last year the Climate Change Commission gave the government its substantial plan to reduce dangerous climate gases.
New Zealand's emissions are static, and international group Climate Action Trackers says this country's reduction efforts are "highly insufficient".
Despite being a rich country that can afford to make cuts we remain one of the largest emitters per capita in the world.
What is the case about?
The Lawyers for Climate Action NZ argue the Intergovernmental Panel on Climate Change - the IPCC - declared in 2018 it was absolutely critical to start slashing emissions before 2030.
But the lawyers contend the CCC's plan actually lets emissions increase over that time - before dropping away and reaching net zero slightly ahead of the 2050 goal.
The lawyers said substantial amounts of damaging gases would be belched out in the meantime, adding to the warming already causing more frequent and devastating storms, and sea level rise.
They said the commission used the wrong calculations in its advice - mixing gross and net emissions in a way that does not compare apples with apples - something the commission rejects.
The lawyers also want the commission to reconsider the advice it gave to the government when it updated its international commitments to slash emissions - called a Nationally Determined Contributions - late last year.
It is expected the lawyers will call climate scientists and academics from here and abroad.
What does the Climate Change Commission say?
Climate Change Commission chair Rod Carr said claims it was not sufficiently ambitious were wrong and misrepresented its advice.
He said its roadmap was evidence-based - meeting reduction targets while recognising the need for an equitable and sustainable transition.
"The point of difference between the parties is how quickly emissions should be reduced between now and 2030," he said.
"The applicant argues that there ought to be deeper and steeper cuts in emissions between now and 2030, regardless of the impact.
"We are confident in our advice and will be rigorously defending it."
Dr Carr said he recognised the intent of the proceedings was to ensure Aotearoa was taking action to address climate change.
Late last year, the commission had another look at its advice to the government and concluded that deeper domestic cuts could bring "damaging and inequitable levels of economic and social disruption."
What does the government say?
Climate Change Minister James Shaw said the hearing promised to be very interesting.
"We are seeing more and more of this kind of litigation around the world, and I do think it is a healthy way to test the system," he said.
What is at stake?
If the court sides with the lawyers it would be a huge win for those pushing for more action on climate change, but potentially only a symbolic one - it all depends on what the judge decides.
The commission could appeal the decision, and even if it is forced back to the drawing board, the government is not compelled to heed the commission's advice.
But having a court rule for stronger action on climate change would put a great deal of pressure on a government that has declared a climate emergency.
It would also be embarrassing for the Climate Change Commission.
The hearing is expected to last the week.
