Witness the life of a statue in New York City. Financial firm State Street begins conversations with the city in 2016 about what will become “Fearless Girl,” the sculpture of a confident child staring down the much larger and more iconic Wall Street bull.

State Street pays $19,625 for a five-day permit. The statue gets installed at the southern base of Broadway, facing the bull. On International Women’s Day earlier this month, pictures of the statue are beamed around the world, a metal monument to the flesh and blood women marching and calling for equality in Manhattan’s streets.

The statue touches a nerve. Critics question the motivations of what is ultimately a billboard for a financial firm — the base of the statue carries the inspirational words “She Makes a Difference” just above “State Street Global Advisers.” But that doesn’t stop people from taking thousands of pictures, or generally enjoying the novelty of the work of art. There is certainly something jarring and hopeful about it.

When people pose in the girl’s defiant stance, you can’t help but imagine that they feel a bit more confident facing down the bulls of the world, too.

Mayor Bill de Blasio’s administration quickly extended the statue’s temporary permit to 30 days (which cost State Street another $65,100). But some people were already looking for more, meaning this story is bound to get tricky.

On Friday, freshman Assemb. Yuh-Line Niou, who counts “Fearless Girl” as one of her constituents, was joined by two human girls plus State Sens. Daniel Squadron and Jo Anne Simon and others presenting a letter signed by over fifty female elected officials asking de Blasio to let her stay. On Saturday, Rep. Carolyn Maloney held her own event doing the same.

De Blasio spokeswoman Natalie Grybauskas praised the “important conversations” the statue has raised and cautioned that installing a permanent sculpture demands a “thoughtful review.”

“We’re exploring the possibility of keeping the Fearless Girl for longer than currently permitted,” Grybauskas said.

You might glimpse the way this is going, with a politically fraught choice ahead for the mayor. Will he risk the annoyance of those elected officials and the rash of headlines — “De Blasio Deports Fearless Girl” — if he forces the sculpture to move along?

De Blasio could use the permitting process as cover. Temporary artwork and exhibitions are usually meant to be temporary, and generally the city is better for it: as with the Prego-sponsored “garden” that briefly took over Chelsea Plaza last year, demonstrating some of the ingredients in a new Prego sauce.

Cool, I guess, but do you want it there forever?

The “Fearless Girl” is better art than the sauce jar, but some critics have questioned what exactly she stands for: Why is she a child, unthreatening, instead of a woman? Why was the sculpture sponsored by this company, which may have its own problems with corporate feminism?

That might not matter to viewers, who roll their eyes at political correctness and say it’s a nice idea, give it a rest. On Friday, one appreciative visitor from Texas, Kim Herrera, 22, used the statue to explain to her boyfriend how “little girls have a lot of pressure.” Some need the statue to show a bolder path.

But that still leaves the question: Should anyone be allowed to pay to make something and then drop it in city streets and see if it sticks?

Actually, that’s basically what happened with the new statue’s partner, the charging bull.

It was placed on the street in a guerilla act by artist Arturo Di Modica in 1989, reportedly in response to that era’s stock market crash and recovery. It has moved slightly over the years, but was never banished, and in the interim has become a premier symbol of New York.

You might argue about what the bull means. A contrarian could say that its powerful visage shows a menacing Wall Street. But more often than not it’s celebrated as a positive symbol of Wall Street’s culture, thanks to movie producers and those tourist cameras. You could then argue that Wall Street doesn’t represent all of New York, and the self-satisfied raging bull is embarrassing to New Yorkers. And sometimes it’s kind of gross. Stand in the traffic triangle for a few minutes sometime and witness how many visitors touch a certain part of its body.

There have been anti-bull moments critiquing this work of art. The Occupy Wall Street movement launched with a poster imagining a ballerina atop the bull, a response that the “Fearless Girl” echoes.

But if you didn’t allow the bull in the first place, you wouldn’t need the girl.

Correction: An earlier version of this column mispelled the name of Assemblymember Yuh-Line Niou. Her name is Yuh-Line, not Yu-Line.