This is not the official Mario timeline. This is a combination of several theories made by many YouTubers mixed in together with my own. Please enjoy.
It all started in an arcade game, simply called "Donkey Kong" where Jumpman had to save Pauline from the original Donkey Kong. Climbing up meters and meters of girders, he finally rescues her and then they get married. About a year later, Jumpman decides to capture OG Donkey Kong and keep him as his "prize". But luckily Donkey Kong Jr. climbed his way up to free his father.
Unfortunately for Jumpman, he died from falling a great height. The Kongs then retreated to their known island. Meanwhile back in the city, Pauline got news that Jumpman had died. But that wasn't the only thing she had her mind on. She was pregnant with twins! Knowing that her husband, Jumpman was an animal abuser she decided that after her 2 children were born, they'd be sent away by a stork to a new family.
And so, it happened. On the night of the twins birth, Pauline decided to name her twins: Mario and Luigi. During her pregnancy she had made them 2 hats that they would soon grow into once they were adults. She put them in a silk bag and had their heads popping out and told the stork to fly far away.
Now we get to the beginning of Yoshi's Island on the Super Nintendo Entertainment System (SNES)
On the island the natives were living a peaceful life. Until something fell onto a Yoshi. Now this wasn't just any normal Yoshi. This was the chief of all Yoshis and that something that had fallen was none other than Baby Mario. He had been knocked out of his silk bag by Kamek the Magikoopa who had taken the stork and his brother, Baby Luigi.
So, the Yoshis went on a relay mission across the island until they got to the enemy base. The chief Yoshi carried Baby Mario one last time (Yeah right) through the castle until they got to a bedroom like throne room. And there was Kamek and his royal highness Baby Bowser. They battled against Baby Bowser in both his phases until he was knocked out.
The Chief Yoshi finally returned Baby Mario to his brother and the stork took the brothers to their new parents.