ALBANY, N.Y. — Governor Kathy C. Hochul, the first woman in history to lead New York, took the helm this week under extraordinary circumstances, as she replaced a disgraced governor and moved to confront staggering public health, educational and economic challenges across the state.

Minutes after sketching out her vision in her initial address as governor on Tuesday, Ms. Hochul — a Western New York Democrat — sat down with The New York Times at the State Capitol. In a wide-ranging interview, the relatively little-known executive discussed her governing philosophy and her plans for the state, her political leanings (“I’m a Biden Democrat”) and her ambitions for her new team (she has decided on her lieutenant governor, she said).

And she offered some of her most extensive remarks to date about how she contrasts with Andrew M. Cuomo, whom she replaced in office following his resignation.

Below are edited and condensed excerpts from the interview with Ms. Hochul, 62, whose remarkable political rise has taken her from local official to congresswoman, and now from lieutenant governor to one of the most consequential jobs in the nation.

You’re making history as the first female governor to lead New York. To what extent does that feel meaningful to you?

I feel a heavy weight of responsibility on my shoulders.

I take it very seriously, my position as first female governor. But I want at the end of my term — terms — to make sure that no woman, no girl, no teenager ever feels there’s anything they can’t do.

How should New Yorkers judge whether your tenure was a success?

Do we get stuff done? I’m direct. I have a very focused agenda. And I hold myself to the highest standards. I judge myself more harshly than any voter, or any New Yorker, will.

Judge me by specific accomplishments in terms of what I announced today and what I’ll announce in the State of the State address, and hold me accountable to those ambitions. But at the end of the day, I want people to say that I played a major role in restoring people’s confidence in the ability of state government to be on their side, to fight for them, and again — I’ll say it again — to get things done.

Are you, as governor, directing teachers statewide to get the vaccine?

I want everyone in the state of New York to get the vaccine, particularly teachers, and people who are in a school environment — or have a testing requirement, frequent testing.

However, the governor does not possess the executive powers that were in place a year ago, so I will be working hard, developing partnerships with these stakeholders who can work with me to get this done.

Governor Cuomo’s response to the pandemic was sometimes criticized for being too top-down and dismissive of public health experts’ advice. How will your approach differ from his?

I’m hard-wired to view everything that Albany does through the lens of a local town, city, county official.

That’s a shift in philosophy. I’m here, ready — I’m going to give you direction; I’ll back you up. But I also don’t want to take away powers that rest with you, because I know what that feels like.

I was in that position when Albany would be so heavy-handed. But I also think a pandemic requires a strong response. I will give strong responses. I’m decisive. And I’ll back everything I do up with consultation with people who are in the field.

What is the appropriate balance between demonstrating executive leadership and deferring to local officials?

It’s consultation with the locals, and then the buck stops with me.

Your predecessor was known to have a heavy hand with the Metropolitan Transportation Authority. How much authority are you looking to assert over the M.T.A.?

I’ve already had conversations with leadership; I’ve been briefed on our significant projects, and I want to get them done.

Authority doesn’t have to be concentrated in me when I’m hiring outstanding professionals who know their jobs. I will be there if there’s something that’s not following what I want. But I also know that day to day, they’re the ones that have to be accountable. Accountable to the riders, accountable to me. But I also know that granting more freedom allows them to rise.

You’ve been in New York politics a long time, but you’ve also been open about the fact that you did not work closely with Governor Cuomo. If you weren’t especially involved in his policymaking decisions, what do you say to people who question whether you have the managerial experience to lead the state forward?

If they have any questions about my ability to lead, speak to every single person who’s in government with me, because they know I bring up a collaborative approach to government. And I know that that is going to be a breath of fresh air. I’ve heard that from countless current employees, cabinet members, heads of agencies, heads of authorities.

Not being in every single room means I was somewhere else learning the state like no other. Nobody knows the state — no person alive knows the state the way I do. That’s because I set out to make this role, redefine it as I have every single role I’ve had. I’ve done that as lieutenant governor, and that’s why I have the breadth of knowledge, relationships and just a deep love for the state.

One thing that was probably not in your job description as lieutenant governor was publicly disagreeing with Governor Cuomo. Now that you are governor, what is one main policy difference that you had with him?

I thought we should have done more with the New York City Housing Authority. I think there’s still an opportunity. So many people are living in squalor. The heat is not reliable in the wintertime. It’s too hot in the summertime. Things are breaking down, and I want to get back to the nuts and bolts. Everybody has the dignity, even the dignity of having a good roof over their heads.

I’ve seen how transformative it is when you give people a safe home, something that so many take for granted, but if you don’t have it, it’s terrifying.

So that’s one area where I would spend more public time and effort.

Do you plan to use your influence to help Democrats expand the House majority through the redistricting process?

Yes. I am also the leader of the New York State Democratic Party. I embrace that.

I have a responsibility to lead this party, as well as the government. I’m going to be doing whatever I can to let people know that the values of the Democratic Party today are part of who I am, fighting for people that just had a tough blow dealt to them in life.

The Democratic Party has to regain its position that it once had when I was growing up. My grandparents were F.D.R. Democrats. My parents were J.F.K. Democrats.

Today, I’m a Biden Democrat.

Are you saying that because he’s the president or because you share similar worldviews?

Because it comes from a view that all of us have a moral responsibility to fight for the underdog.

That’s what I’ve done my whole life. To engage in policies, like fighting for the Affordable Care Act, which I did — which led to my demise in Congress. The core value is fighting for people, for health care, for helping them get out of this pandemic.

I’m eager to lead that party and use the power that I have to help make sure there are more Democrats there to help Joe Biden get his agenda through the Senate. I just spoke to Senator Schumer a short time ago. I talked to Joe Biden last night. Nancy Pelosi has called me a couple days ago.

So these are relationships I have, but I also take seriously my job to increase their numbers so the Democratic agenda gets through and is there to help the American people.

Have you decided whom your lieutenant governor will be? Yes or no?

[In a hushed voice, with an almost-wink] Yes.

Who?

Stay tuned.

Do you support the congestion pricing plan for New York City, and do you want to accelerate its implementation?

I’ve supported it from its inception.

I believe it has to happen for all the reasons we know congestion pricing works. But I also got to work on finding out the rollout time. I know they’re saying from 18 months to 16 months, but I want to check into that.

Do you agree with Eric Adams, the Democratic nominee for New York City mayor, that changes should be considered for the state’s bail law, and if so, what do you believe should be changed?

I’m not sure the bail law is being implemented the way it was intended.

Judges have far more discretion to ensure that people meet the standards put forth in the law so no one who’s been convicted of a violent crime is able to get out. The law spells out what’s supposed to be in place for judges to evaluate, and I’m not 100 percent sure that’s what’s happening.

So I’ve not seen evidence — and I support bail reform, support it strongly, because we’ve had an unjust system. Same crime, two people. One’s rich, one’s poor. One’s going to jail, one is staying at home. I’ve said for years how un-American that is.

We also have a responsibility to protect our citizens and protect our communities, so I’m willing to look at that.

Governor Cuomo said that the attorney general’s report was unfair and politically motivated. Do you think he had adequate due process?

I had full confidence, from the very beginning, in the attorney general’s report. I have confidence in the conclusion and the results.

Do you think you’d beat him in a primary next year?

I have a very good record of winning elections, especially the ones that people tell me I can’t win.

You’ve spoken with a lot of national leaders in recent weeks, including Hillary Clinton. What advice did she give you?

“Stay strong.”

She was so gracious in offering to be there as a sounding board, talk whenever I wanted to.

I’ll never forget, when I won my special election in Congress, I got my head kicked in.

So after that, I’m battle-scarred. Hillary has been through the same. There aren’t many people who’ve been in those trenches. It creates a special bond.

That’s what I talked about with Hillary — changing people’s images of women in executive positions. And that’s what I want to do.