Sunday's visit of Parma not only marks the start of both clubs' league campaigns but will be the first Serie A match to be played at the Bianconeri's new 41,000-capacity Juventus Arena.
The Turin giants are the first Serie A team to own their stadium following years of renting the Stadio Delle Alpi and then the Olympic stadium.
"We have great expectations," said Del Piero. "We know that if we give our best, we can dream.
"Following our recent campaigns, we have to start with our feet on the ground, without suddenly thinking about the top.
"There will be a time when we can start to fly but we have to remember that many changes have taken place.
"We have a new coach, so many new players and a new stadium.
"These significant changes should create enthusiasm and it's from there that we begin our campaign, with the dream of returning to have winning seasons."
Under new coach Antonio Conte, Juve are looking to improve from successive seventh-placed finishes that saw them miss out on the Champions League two seasons in a row.
Opponents Parma have strengthened their team with the arrival of 12 new players this summer.
Franco Colomba's side finished 12th last term and despite the numerous reinforcements, the team's primary goal is to maintain its top-flight status.
"Our aim is the same as last year," said Parma striker Hernan Crespo.
"We have to be smart and keep our feet on the ground.
"We just want to focus solely on avoiding the drop and the sooner we do it, the better."
Former Juventus winger Sebastian Giovinco will lead Parma's attack alongside Graziano Pelle.