The case, led by two teenagers and supported by the "Digital Freedom Project" argues banning kids from social media as it infringes on implied freedom of communication.
The ban takes effect on Wednesday - the deadline for social media platforms to restrict Australians aged under 16 from holding accounts.
The law applies to 10 platforms, including Facebook, Instagram, TikTok, Snapchat and X, and is aimed at protecting children from online harms.
NSW Premier Chris Minns said his government would join South Australia in intervening in the proceedings after being a leading advocate for stronger protections for children online.
"I've said before, social media is this giant global unregulated experiment on children," Mr Minns said on Monday.
"These laws put responsibility where it belongs – on the platforms themselves. If they fail to protect young people, there must be consequences.
"We will seek to be heard in the High Court challenge because the principle at the heart of this reform is simple: when something threatens to harm our kids, we act."
Several smaller apps are growing in popularity as children migrate to those not included in the ban.
They include Lemon8, which has agreed to restrict use of its app to those 16 and older as of Wednesday.
Voters have thrown their support behind the ban but are not confident social media companies will comply, according to polling conducted by Resolve Political Monitor for the Sydney Morning Herald.
Nearly 70 per cent of those polled backed the ban but only 35 per cent are confident that users under the age of 16 will be effectively blocked.
Less than 30 per cent of parents planned to fully enforce the ban by deleting apps off their kids phones and 53 per cent said they would pick and choose what their child could access.
Prime Minister Anthony Albanese said on Sunday the world first initiative had already won support in Europe, Asia and others were expected to follow Australia's footsteps.
"I think it is a success already because what's happening is that parents are having this discussion with their young ones," he told ABC Insiders.
"It's happening in schools; it's happening with parents having those discussions with children. It's happening as well, to hold these social media giants to account."
Labor has met repeatedly with parents including Emma Mason, the mother of 15-year-old Tilly, who took her own life after being bullied online.
The coalition has ramped up its criticism of the ban, with Nationals leader David Littleproud unconvinced tech giants will comply.
Platforms face up to $49.5 million in fines if they do not take "reasonable steps" to prevent under-16s from holding an account.
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