Super Mario World 2: Yoshi's Island

Super Mario World 2: Yoshi's Island was the birth of Mario & Luigi and the rocky road it took for them to be delivered to their parents.

History
A Stork hurries across the dusky, pre-dawn sky. In his bill, he supports a pair of brothers; Mario & Luigi. Suddenly, Kamek ambushes the stork in a gap between the clouds with blinding speed in an attempt to catch both babies. Although Luigi managed to be captured, Mario fell undetected toward Yoshi's Island and onto the lap of a Yoshi. Kamek, meanwhile, quickly dispatches his gang of Toadies to search for the remaining infant.

Collecting everyone, the Yoshi clan are in uproar about what to do with Mario. As it turns out, the infant does know where Luigi is via a form of brotherly connection. Thus, the Yoshis decide to send him to his location via a Yoshi-to-Yoshi relay system.

At one of his many encounters, Kamek reveals to the Yoshis that Luigi is being held at Bowser's Castle at the Koopa Kingdom. After finishing up the rest of the castles on their island, the Yoshis warp to the Koopa Kingdom in a white flash of light.

The Yoshis then make their way through Bowser's Castle, arriving at Bowser's room and having a tussle with the infant Bowser. Kamek then showers Bowser in magic, making him grow to a size that causes the castle to crumble down around them. Yoshi shoots Bowser down, returning him back to size. Kamek grabs the defeated youth and flies away, promising to return one day.

Despite his threat, Mario had been reunited with Luigi and the Stork who was tied up. Save from all threats, the Stork could peacefully deliver the brothers to their correct parents, probably.

Timeline

 * Mario & Luigi have just been born and are being delivered to their home by a stork, placing this game prior to all other games featuring the brothers.