Senator Babet was the sole parliamentarian elected from Clive Palmer's ticket after defeating the Liberals' Greg Mirabella.
"I stand here as someone who has not been groomed in the political machine," Senator Babet told the chamber on Wednesday.
"I was not a staffer. I was not a long-term member of a major political party.
"What I am is a regular Australian who decided it was time to put my hand up and have a go. A regular Australian who felt like I needed to do something to have my voice heard."
The Mauritius-born Victoria senator took aim at the "decline of traditional institutions" such as marriage, religion and family.
"Radical Marxist ideology has been marching through our institutions for some time," he said.
"Terms like white privilege and gender fluidity have now become commonplace.
"Marxists see the world as being inherently unequal. They seek to address this apparent inequality by tearing down the very fabric of our civilisation."
He concluded his speech by shouting "Aussie, Aussie, Aussie", to which people in the gallery retorted "oi, oi, oi" before being cut off by the Senate president.
It followed the first speech of Greens senator Barbara Pocock, who spoke of a political awakening as voters turned away from the major parties.
Senator Pocock called on the parliament to establish a more equitable system after people voted for "a politics of hope".
"Markets make good servants but bad masters. They deny care," the South Australian senator said.
"The logic of the market, cost minimisation and profit maximisation, creates childcare deserts. It makes gender and racial discrimination profitable. It drives the greedy exploitation of new reserves.
"My generation had every advantage. Thirty years of continuous economic growth means our kids deserve the same, so I'm here so that I can look future generations in the eye and say I did everything I could."
Senator Pocock also advocated for an Indigenous Voice to parliament but warned against ignoring the wishes of First Nations people when it comes to treaty and truth-telling.
"We talk about Voice. But we must listen to First Nations voices now, and do no fresh harm by ignoring their wishes and their connection to country," she said.
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