After winning their second Super Bowl under Coughlin, the Giants have missed the playoffs the past four seasons. They have posted losing records for three straight seasons, including 6-10 in the past two.
"The most important thing, when we talked about leadership, is you've got to be yourself -- everybody else is already taken, including Tom," McAdoo said Friday at his introductory press conference. "So I can't worry about being in Tom's shadow. I've got to be comfortable in my own skin, and I am that."
The Giants officially announced McAdoo's appointment on Thursday, preferring the 38-year-old over the five other candidates they interviewed. Only recently hired Miami Dolphins coach Adam Gase (37) is younger among NFL head coaches.
McAdoo is expected to keep the coaching staff largely intact from last season under Coughlin, who resigned on Jan. 4 after leading the Giants for 12 seasons.
"This is the capital of the world, and the football capital of the world and with that comes a certain amount of pressure, pressure I look forward to," McAdoo told reporters Friday. "We're not looking to rebuild. We're looking to reload and that's going to start in a few minutes."
McAdoo offered a preview of what to expect from him as head coach.
"This is the opportunity of a lifetime. I was brought up in this business to keep your head down and keep working," McAdoo said. "This job is not for the faint of heart. I'm the right man for the job.
"At the end of the day we're paid to win, not just compete. The vision for this football team is putting a fifth Lombardi Trophy in the case."
McAdoo was the Giants' offensive coordinator the past two seasons under Coughlin.
Veteran quarterback Eli Manning was among the players who quickly endorsed McAdoo. Promoting McAdoo also keeps Manning playing in a familiar offense. Manning passed for a career-high 35 touchdowns in 2015.
The Giants scored just 294 points the season before McAdoo was hired to run the offense. New York scored 380 points in 2014 and 420 this past season -- the latter ranking fifth in franchise history.
"We're going to take a look at last season and study every game and situation ... figure out what we can do in all three phases," McAdoo said.