Perhaps Peter meets Thor when the Avengers are having a recruitment drive. Thor is initially skeptical of this young 'Spider - boy' as he might call him. But as they train together, Peter's agility and Thor's strength complement each other. They end up on a mission together where Peter has to use his webs to save Thor from a fall, and Thor in turn uses his lightning to power up Peter's suit for a short time. This experience makes them respect each other more and they start to bond.
One possible plot could be that Peter, being his curious self from Queens, stumbles upon Thor in a strange situation. Maybe Thor is trying to adapt to life on Earth without his powers for a while. Peter, with his quick thinking and scientific knowledge, tries to help Thor figure out what's wrong. Along the way, they form an unlikely friendship, with Peter constantly asking Thor about Asgard and Thor learning about the modern world from Peter.
Maybe in the fanfiction, MCU Peter is on a mission when he accidentally stumbles into a portal and ends up in the world of another Peter. They start comparing their lives, like how different their love interests are. MCU Peter could learn some old - school web - slinging techniques from the other Peter, and they end up having to fight a villain that threatens both of their worlds, leading to a great team - up.
In a 'Thor meets Wonder Woman' fanfiction, perhaps they meet in a neutral realm. Thor is intrigued by Wonder Woman's connection to the Greek gods while she is curious about his Asgardian heritage. They get involved in a tournament of sorts where they have to team up against other powerful beings. During this time, they share stories of their heroic deeds. Thor tells her about his battles against the Frost Giants and Wonder Woman shares her tales of protecting the world from Ares. By the end of the tournament, they exchange gifts - Thor gives her a small Asgardian charm and she gives him a piece of Amazonian armor.
Well, perhaps Thor and Richard could meet in a modern city. Thor is on a mission to retrieve a powerful artifact that has been smuggled into the human world. Richard, who is an expert in ancient relics, unknowingly has the key to finding this artifact. Their meeting could start with Thor saving Richard from some thugs who are after the same artifact. And then they team up to find the item before it falls into the wrong hands.
One possible plot could be that Peter discovers his true parentage as Thor's son later in life. This revelation could change his entire perspective and lead him to Asgard to learn about his heritage.
The plot might involve Thor being banished to a dimension similar to Earth where Donald Blake lives. At first, Thor's brash Asgardian ways clash with Blake's more reserved and scientific approach. But as they get to know each other, they find common ground. For example, they both care about the innocent. They then discover that a dark entity is trying to open portals between their two worlds to cause chaos. So, they must combine Thor's strength and Blake's intellect to stop this threat and in the process, become great friends.
One possible plot could be that Peter Parker, while on a school trip or some scientific research in space (maybe with Stark tech), accidentally stumbles upon Peter Quill and the Guardians of the Galaxy. They initially have a bit of a misunderstanding as their ways of doing things are quite different. Parker is used to the more down - to - earth (literally) problems in New York, while Quill is dealing with intergalactic threats. But they soon realize they can learn from each other. Parker could teach Quill about the latest Earth - based technology, and Quill could show Parker the wonders of the galaxy.
Well, one possible plot could be that Peter is sent to Wakanda on a mission by Stark (before his death perhaps). There he meets Shuri. Shuri is initially skeptical of this young outsider but as Peter shows his intelligence and skills (like his web - shooting tech), she warms up to him. They then work together to improve some of Wakanda's security systems using Peter's unique perspective on technology.
One possible plot is that Peter is exploring some strange part of the city, perhaps an alleyway that has some sort of magical anomaly. Loki, who is also drawn to the magic, appears. Peter is initially scared but then realizes Loki might not be there to cause trouble right away. They could end up teaming up to solve the mystery of the strange magic, with Loki teaching Peter some things about magic along the way.
Well, perhaps Jack Frost accidentally enters Neverland while chasing a particularly strong winter wind. Peter Pan mistakes him for a new kind of fairy at first. Then they start to compete in various things, like who can fly faster (Jack using his ice - made wings and Peter with his pixie dust). But as they get to know each other, they realize they have a common enemy in Captain Hook, who wants to use Jack's ice powers to freeze the mermaids' lagoon and catch them easily. So they have to work together to stop Hook.
One possible plot could be Peter growing up in Asgard, learning the ways of the Asgardians and struggling to control his powers which are a mix of his own and those he might inherit from Thor.