The world-leading restrictions kick in on December 10, with children set to be booted from platforms including Instagram, Facebook, Snapchat and TikTok.
In a statement on Wednesday, the Digital Freedom Project announced it had launched proceedings in the nation's highest court in a bid to overturn the laws.
The group will challenge the ban on the grounds it "robs" more than 2.5 million young Australians of their constitutional implied right of political communication.
The Australian constitution does not explicitly protect freedom of speech.
Teens Noah Jones and Macy Neyland, both aged 15, are listed as the plaintiffs.
Digital Freedom Project president and NSW parliamentarian John Ruddick labelled the ban disproportionate, saying it is "a direct assault on young people's right to freedom of political communication".
"It is not the government's role to parent children, it should be up to families to decide when their children are ready for social media," he said.
"This is the most draconian legislation of its type in the world.Â
"Even the Chinese Communist Party would be drooling over this."
The group described the legislation as "grossly excessive".
Social media companies face fines of up to $49.5 million if they fail to take "reasonable steps" to block young users from the cut-off date.
Platforms must implement age-assurance technology, but the eSafety Commission has not outlined a specific type or method.
Communications Minister Anika Wells has previously said the list would be fluid, meaning more platforms could be added.
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