The Danish driver gave Haas an incredible finish in the Bahrain Grand Prix on Monday, qualifying in seventh place and finishing P5.
McLaren was plagued by brake cooling issues throughout the pre-season, which continued into the season-opening Bahrain Grand Prix.
They appeared to be a notable victim of the "porpoising" issue that many teams have experienced as a result of the new technical regulations.
Halfway through the hour, the reigning champion switched to soft tyres and set the fastest time with a time of 1m 31.936s.
The rule, which was implemented in 2014, required all drivers who advanced to Q3 to start the race on the same tyres they used in Q2.
It will be Hulkenberg's first Grand Prix since standing in for Lance Stroll at Racing Point at the 2020 Eifel Grand Prix.
The Frenchman also revealed that he would not have been able to keep up Hamilton if they were in their 2021 cars.
Many teams, including the reigning constructors' champions, Mercedes, appear to have been caught off guard by the aerodynamic phenomenon.
Drivers have had to spend most of pre-season testing getting to know the cars and a unanimous verdict is that following is a lot easier.
The British team already has a deal with Mercedes that allows them to borrow Stoffel Vandoorne or Nyck de Vries when needed.