But I think OP means a Green-led government. And to achieve that you need a Green-SPD-Left-coalition which isn't impossible, but you seriously will have to alter Germany and the Greens because at the moment the Greens lack the ability to be a "people's party" which is able to reach out to all kind of voters.
The era of "people's parties" is over in German politics. With a little bit of luck, the Greens have a chance in the next elections.
While lacking strength in rural regions and East Germany, the Greens are currently on a path of becoming the strongest party in West German cities, since both the CDU and the SPD have problems attracting urban voters.
The CDU is currently moving away from the more centrist Merkel-Ära back to more conservative roots. This alienates moderate urban voters and slowly transforms the CDU into a more rural party. Meanwhile the SPD is unable to regain its previous strength, since traditional social democratic milieus vanished. Meanwhile far right voters won't vote for the CDU/CSU as long as the AfD is available.
In Baden-Württemberg, the Greens are already in the position of a "people's party", on the state and communal level. Several larger cities in Germany have green mayors. Younger voters have a stronger tendency to vote the Greens, while older voters prever CDU or SPD.
My POD would be no Corona Crisis, and later Friedrich Merz as the next leader of the CDU. Merz fails to attract centrist voters during the 2021 federal elections. A hot summer strengthens the Climate Protests. Result: The Greens gain 25% with a weakened SPD. While the CDU has a better result with somewhat above 30%, a Green-Red-Red coalition forms.
Let us now greet Chancellor Robert Habeck.