The short answer of how George and Lennie started traveling together is that "it just happened." This is probably the most profound and truest answer. In the world of poverty, people don't really make choices. Things just happen. Options, decision, and weighing choices exist only in a world where opportunities exist. From this perspective, the ability to choose is a luxury.
In a conversation with Slim, George explains his relationship with Lennie. He says that they were born close to each other in Auburn. George knew his Aunt Clara. When Aunt Clara died, Lennie just tagged along. They worked together, and they got used to each other. There is nothing profound. Here are the words of George.
“Him and me was both born in Auburn. I knowed his Aunt Clara. She took him when he was a baby and raised him up. When his Aunt Clara died, Lennie just come along with me out workin’. Got kinda used to each other after a little while.”
The paradox of George and Lennie is that they are the only friends in the book. So, what "just happened" turned out to be one of the great bright spots in the book.