seeing that he is his godfather and their parents are so close, sirius would have known harry ever since he was born. but it was not till harry's third year when sirius finally met the grown up Harry.
Sirius gave Harry his first broomstick which could hover two feet off the floor for his first birthday. After Voldemort attacked the Potters, Sirius met Hagrid with 15 month old Harry and wanted to take him, being his godfather. But Hagrid said that he was under Dumbledore's orders to deliver Harry to his Aunt Petunia in Little Whinging. So Sirirus loaned Hagrid his flying motorbike for the journey as Hagrid was too heavy to ride a broom. The next time Sirius met Harry, he was thirteen. They knew each other for two more years until Sirius was killed.