A former policeman, mechanic, striker and now touchline prowler, Baumgart has developed cult status in German football during spells in charge of Paderborn and now Cologne, nurturing his own style in terms of both play, coaching passion and dugout fashion.
"I always wanted to be a coach," the 50-year-old told bundesliga.com. "It sounds dumb, but it was never my goal to be a player in the Bundesliga. I just wanted to play football for a long, long time. My goal was always to be a coach."
That being said, he still made over 350 appearances across 14 years in the Bundesliga and Bundesliga 2, scoring the winner on his debut for hometown club Hansa Rostock against Hertha Berlin on the opening day of the 1994/95 season in the second division.
The East German native would score 64 times in spells with Rostock, Wolfsburg, Union Berlin and Energie Cottbus - all this after working for a year with the riot police and later re-training as a mechanic whilst an amateur footballer before Hansa picked him up.
One of his goals came against Bayern Munich and Oliver Kahn for Cottbus in 2006/07. "I even got his shirt after the game," Baumgart remarked before mentioning a fact that seems to have haunted him - and in fairness most players and coaches in Germany - about facing the record champions: "And it ended like it always does."
That's because Baumgart's header to make it 1-1 in the second half meant nothing as Daniel Van Buyten restored Bayern's lead 60 seconds later. A familiar theme for Baumgart's teams as a coach, who have generally scored against the Munich club but still been beaten. He's lost 3-2 in three out of five encounters.
It's that attacking mentality of 'yes, we'll concede but we're going to score more than you' that has endeared him to fans. He even says it in the above video of him having to watch a game at home while isolating.
The swashbuckling approach saw him guide Paderborn to back-to-back promotions from the third division all the way to the Bundesliga. Although their top-flight stay only lasted a year, he remained with the club and they remained loyal to him.
It was a whirlwind four years that actually looked like beginning in tears after failing to save Paderborn from relegation to the fourth tier after taking over in April 2017. But they were handed a lifeline due to 1860 Munich being denied a place in the third division and going straight down to the fourth after relegation from Bundesliga 2. The rest, as they say, was history.
It was during his first stint in the Bundesliga that his effervescence on the touchline really came to light. For example, he became the first coach to receive a yellow card in the top flight following the introduction of that rule.
It's behaviour that can be nicely summed up in one line of his that was named Football Quote of the Year 2021 in Germany: "A game's only over when the ref blows his whistle and I stop yelling."
It came about following an altercation with striker Anthony Modeste where Baumgart berated the forward with three minutes of a game to go. Not that there are any hard feelings between the two. In fact, the pair were involved in a now famous incident where Modeste grabbed the coach's cap and danced with it on to celebrate a goal. Although Baumgart was annoyed, he insists it wasn't to do with having his cap stolen.
"You can grab my cap. That was a good moment, but the moment wasn't over," he once explained. "I wasn't annoyed because… I always find the interpretation others make quite funny. I was more annoyed about the game, that we'd scored a late equaliser. I was annoyed because we'd been behind. It was 2-2 [against Union Berlin] and we had four minutes left. It was actually about us keeping going."
In fact, Baumgart's cap has earned its own legendary status around Cologne and German football in general. During his time at Paderborn, his headwear of choice was a baseball cap. Now the most famous attire on Bundesliga touchlines is his flat cap - so much so that he once swapped it for Manuel Neuer's jersey, against whom he once played while with Cottbus when the goalkeeper was coming through at Schalke.
As the Billy Goats boss explained: "I've always wanted a Manuel Neuer shirt. My daughter has wanted one for a long time as well. And he asked for my cap in return. It all worked out."
Neuer also went on to state that the "legendary" cap will have "pride of place" in his collection.
But why a flat cap?
"I like wearing hats in general. I think it's a lot to do with the fact I don't really like my hair. I don't like putting stuff in my hair," Baumgart explained. "You'll very rarely see me with hair wax or something. I don't have hair that looks like it's been styled, just a bit wild. And I just think caps suit me. I don't care if people like that. And flat caps are a hat that just suit me.
"It's always good when a trademark comes from something you didn't intend, and just happens naturally. Okay, the flat cap is a thing now, it's a special cap. Like with many things, it just happens. I like baseball caps for some things, the flat cap for others. I often have a baseball cap on for training, and now I wear the flat cap in stadiums. I think it suits me."
His caps and club attire are made distinctive thanks to the number 72, his year of birth, instead of the usual initials that most coaches have. Both now hold cult status around Cologne the club and the city.
No matter the weather, his matchday outfit is no more than a polo shirt with a gilet and his cap - regardless of the freezing winter temperatures or driving rain. There are billboards around the Cathedral City bearing his face and cap to advertise various products. Remember, he only joined the club in summer 2021.
His impact on the team, who had only avoided relegation thanks via the play-off last season under Friedhelm Funkel, to have them now competing for European qualification has been remarkable and appreciated beyond belief by Cologne supporters.
They love what he has done to the team (unsurprisingly) and also how he's taken to life in the city - especially his first Carnival.
"If you get involved with Cologne, they you also get involved with Carnival," Baumgart said of his now infamous appearance at training dressed as a pink unicorn.
And to top it, his coaching staff all paid homage to their boss by dressing up in his now distinctive style. An outfit that was reportedly one of the most popular at Carnival festivities in the city this year.
"I think there are worse things than making a fool of yourself from time to time," he said afterwards.
But for Baumgart, it's all fun and games until the game itself is underway. Then it's 90 minutes of utmost commitment, both from his players and himself. And as we've seen, it doesn't even need to be on the touchline.