But a strong police presence at the park also prevented the group from congregating in one location and organisers eventually urged people to leave the area.
A number of officers, including some on horseback, were photographed guarding a nearby statue of James Cook.
In a media conference following the event, NSW Police Assistant Commissioner Mick Willing said 600 police officers outnumbered protesters two to one.
"As you've seen this evening a significant police presence was put on the ground to deal with any eventuality when it came to what was an unauthorised public gathering," he said. "It's disappointing to acknowledge that around 300 people chose to ignore the warnings."
A 24-year-old woman was arrested after failing to comply with a move-on direction. She was subsequently fined for breaching a public health order and released.
One of the organisers, Rachel Evans of the Indigenous Social Justice Association (ISJA), told SBS News ahead of the rally that the group planned to "be like the river" to avoid breaching restrictions.
"Like the Hong Kong movement that shifts and turns. We are not going away," she said.
The Facebook event for the rally said the action was in support of inmates at Sydney's Long Bay jail after correctional officers used tear gas in response to a disturbance earlier this week. Following the incident, inmates used materials to spell out 'BLM' - a reference to the Black Lives Matter movement.
Assistant Commissioner Willing previously warned that officers would not hesitate to prosecute those who attended the protest in breach of COVID-19 regulations.
“I want to be clear about this – if people choose to break the law and attend this protest, police will not hesitate to take the appropriate action against them.”
Prime Minister Scott Morrison on Friday also urged people not to attend protests over the weekend as they were against health advice.
"The medical advice is that this is an unsafe thing to do. It puts not only your own health at risk, but it puts other people's lives at risk," he said.
Organisers had encouraged anyone attending the rally to wear a mask, carry hand sanitiser and maintain physical distancing.
The protest was set to take place hours after Mr Morrison announced plans to allow crowds of up to 10,000 people at sports stadiums with capacities of 40,000 by or less by Jule as part of the third stage of lifting COVID-19 restrictions.
On Thursday night, the NSW Supreme Court blocked a refugee protest scheduled in Sydney on Saturday, approving the NSW Police bid to prevent it going ahead.
Justice Michael Walton ruled that the public health risks, namely the potential spread of coronavirus, outweighed the right to protest.
A similar show of police force will be on standby on Saturday to "deal with anything that confronts them", Assistant Commissioner Willing said on Friday.
"Do not come into the city ... we are still in the midst of a health crisis and we need to obey the directions of the health officials," he said.
Meanwhile, on Friday, Victoria Police confirmed they had fined three organisers of last Saturday's Black Lives Matter rally in Melbourne $1,652 each for breaching coronavirus restrictions.
No further fines would be issued in relation to the protest, a Victoria Police spokesperson said.