Their success in the last HSBC tournament on the world circuit in Los Angeles two weeks ago adds to the favouritism.
New Zealand will open their knockout campaign by playing the winner of the Scotland-Jamaica game on Friday (SA time).
New Zealand has won the Melrose Cup, the prize for Rugby World Cup Sevens, three times, in 2001, 2013 and 2018, the only country to have achieved the feat.
Kurt Baker was part of the New Zealand teams that won in 2013 and 2018, and he believes the side can do it again in 2022.
Baker told rwcsevens.com: "There's always expectation with our team. We put it on ourselves to go and win tournaments, whether it's the World Cup, the World Series, or whatever.
"There's no hiding from the fact that we are expected to win, but we also expect ourselves to win. It is pretty exciting to have the potential to get three in a row, but there's a fair amount of water to go under the bridge before we do it."
New Zealand missed the first four tournaments of the latest world series but took silver medals in their first tournaments back in Singapore and London, before they claimed the Los Angeles title. That was Baker's 50th tournament for the All Blacks Sevens. They also took a bronze medal at the Commonwealth Games tournament.
It had been difficult for all teams coping with Covid-19, but New Zealand had been hampered by being unable to get meaningful competition for longer than other sides.
"Whether that's the reason why we've taken a while to hit our straps, I'm not sure, but I suppose we left LA last week on top which is always good going into a tournament like the World Cup.
"We just clicked. There are a lot of things we have been working on technically, and I suppose our group has changed a fair bit over the last 12 months from tournament to tournament.
"There are some new young guys, who are exciting players, who hadn't had opportunities. I think it came to the point [in Los Angeles] where everyone had a bit more time in the saddle.
"We had our backs against the wall a bit, too, when we were down a few men early in the tournament, so we had no other choice but to put our hands up," he said.