Leverkusen appointed the former Denmark manager on Monday on a two-year contract following the dismissal of Erik ten Hag.
Hjulmand has his work cut out with Leverkusen having failed to record a league win so far and with the in-form Eintracht Frankfurt visiting on Friday.
"It is a big challenge because in football you need processes to make that work," Hjulmand told a press conference. "You don't push a button. You have to work every day and create.
"There is so much quality. We are looking to make that work and tick. Suddenly, it will hopefully explode. We don't know when. Until then we will have good minutes, bad minutes ... and make it work."
Leverkusen lost their opening league fixture 2-1 at home to Hoffenheim before drawing 3-3 with 10-man Werder Bremen, leading to Ten Hag's departure.
The Dutchman had replaced Xabi Alonso in May after the Spaniard left to take over at Real Madrid.
Leverkusen secured the double in the 2023-24 season under Alonso, winning their first Bundesliga title without losing a game, capturing the German Cup and reaching the Europa League final.
However, a summer exodus of key players, including Florian Wirtz, Jeremie Frimpong, Jonathan Tah, Granit Xhaka and Amine Adli has made the task of building on Alonso's success an uphill battle.
Leverkusen spent around 170 million euros to rebuild their squad, bringing in Ibrahim Maza, Malik Tillman, Jarell Quansah, Loic Bade, and Mark Flekken, among others.
"If you want to be a top team you have to be good at almost all facets of the game," the 53-year-old Hjulmand said. "I have the feeling I can be myself here. I don't have to explain how I want to play football, how to lead.
"There have been changes but also very, very good players are left. It is up to us to create a fantastic team on and off the pitch," he added.