Julian Nagelsmann's men came flying out of the blocks and went into the half-time interval with a three-goal advantage to their name, as Florian Wirtz and Jamal Musiala struck before Kai Havertz's penalty.
The Arsenal man stepped up to the spot after Ryan Porteous's red card-worthy foul on Ilkay Gundogan, and the 10 men of Scotland conceded twice more in the second period to Niclas Fullkrug and Emre Can either side of an Antonio Rudiger own-goal consolation.
Here, Sports Mole provides a match analysis of Germany's emphatic victory in Munich, including highlights, our man of the match and the key stats.
HIGHLIGHTS
1st min: Germany fashion a chance inside 55 seconds as Rudiger's long ball picks out Wirtz's run, but Angus Gunn saved with his head before the flag goes up.
10th min: Toni Kroos plays a magnificent cross-field ball out to Joshua Kimmich, who picks out Wirtz inside the D, and the playmaker's first-time hits Gunn's palm and the post before trickling in. 1-0.
19th min: Germany strike again in a flash; Gundogan's beautiful half-turn sparks a rapid attack, as the Barcelona man lays off Havertz. The Arsenal attacker elects to hold the ball up rather than shoot and cuts back to Musiala, who rifles in the hosts' second into the roof of the net. 2-0.
25th min: Clement Turpin blows for a penalty as Ryan Christie clumsily brings down Musiala, but a free kick on the edge of the box is awarded instead following a VAR review. Gunn safely gathers Havertz's low set piece.
31st min: First yellow card of the tournament as Robert Andrich slides in and catches Scott McTominay late.
32nd min: Musiala has the ball in the back of the net, but Turpin's whistle had long gone for a handball against Havertz.
45th min: Gundogan has a close-range header saved by Gunn before being on the receiving end of a shocking challenge from Porteous, who is sent off. Havertz steps up to the spot and sends Gunn the wrong way. 3-0.
48th min: Anthony Ralston goes into the referee's book for a desperate lunge on the tricky Wirtz.
51st min: Rudiger tries one from range and Gunn does not take any chances, tipping the ball round the post for a corner.
58th min: Wirtz spurns a brilliant chance for a fourth, volleying just over the bar from a Maximilian Mittelstadt delivery to the back post.
62nd min: Jonathan Tah catches Christie late and sees yellow.
68th min: Germany substitute Fullkrug hammers home the hosts' fourth into the top corner from the edge of the box after a lucky break off of Grant Hanley. 4-0.
76th min: Hanley hits the ball off of Fullkrug's thigh, and despite Gunn's best efforts, the ball trickles over the line before the offside flag goes up.
87th min: Something for the Scotland fans to cheer as Germany fail to deal with a free kick, and Scott McKenna's header takes a deflection off of Rudiger and deceives Manuel Neuer.
90+3 min: The hosts cap off the biggest opening win ever at a European Championships, as Can is given too much time and space to shoot on the edge of the box and curls into the bottom corner with a helping hand from Gunn.
MAN OF THE MATCH - JAMAL MUSIALA
Special mentions certainly go to Havertz and Wirtz, but Musiala - now Germany's youngest-ever male scorer at a European Championships - was effortlessly gliding across the field throughout his exceptional display, which he capped off with a powerful drive into the roof of the net.
The Bayern Munich youngster also nearly won his side a penalty in the first half and was influential in his nation's third and fourth strikes with his dancing feet, completing five dribbles and also registering a 100% pass accuracy.
STANDOUT MOMENT
Before earning the unwanted honour of receiving the first red card at Euro 2024, Ryan Porteous had actually stopped Jamal Musiala in his tracks in a promising start, only to undo that early hard work with an absolutely shocking tackle on Gundogan.
The Watford man could have done some serious damage to his Barcelona colleague, and his sending-off extinguished any hopes of a Scotland revival, however wafer-thin they already were.
BEST STAT
MATCH STATS
Possession: Germany 73%-27% Scotland
Shots: Germany 20-1 Scotland
Shots on target: Germany 10-0 Scotland
Corners: Germany 5-0 Scotland
Fouls: Germany 15-9 Scotland
LINEUPS
GERMANY (4-2-3-1): Neuer; Kimmich, Tah, Rudiger, Mittelstadt; Kroos (Can 80'), Andrich (Gross 46'); Musiala (73'), Gundogan, Wirtz (Sane 63'); Havertz (Fullkrug 63')
TEAM B (FORMATION): Gunn; Hendry, Porteous, Tierney (McKenna 77'); Ralston, McTominay, McGregor (Gilmour 67'), Robertson; McGinn (McLean 67'), Christie (Shankland 82'); Adams (Hanley 46')