Inspired by Haaland, Dortmund rallied from 3-1 down to record a 5-3 away win on Saturday that will live long in the memory.
The Norway international came on for Lukasz Piszczek after 56 minutes and netted with his first touch 183 seconds later with a low shot into the far corner.
The 19-year-old joined BVB for a reported €20million from Salzburg amid competition from Manchester United and a host Europe's top clubs.
Favre knew he had a top prospect on his hands, but could not believe Haaland's exploits, especially given the youngster had limited training time due to a knee injury ahead of his substitute appearance.
"He has started very well," Dortmund head coach Favre told Sky. "He immediately showed his strengths with his runs in behind, and of course he scored three goals which is incredible.
"He moves well between the lines, which gives us another way of attacking. He was very good and did very well.
"At 19 years old, he has a huge potential for improvement, that's the most important thing. It was a crazy game."
Dortmund play Cologne on Friday and Favre was asked whether Haaland would land a place in the starting line-up.
He added: "The players always say they are ready to play, but he didn't train at all in December because he had a knee injury and couldn't do much in our training camp for three or four days.
"He was not yet ready to play 90 minutes [against Augsburg]. We will see about Friday."
Dortmund captain Reus was equally excited about the early signs from Haaland.
"Erling is very calm, but very ambitious," said Reus.
"He trains incredibly hard. I think the last person to make his debut in Augsburg was Auba [Pierre-Emerick Aubameyang], and he also scored three goals.
"He has made a good impression and had a great debut."