So …. the Atlanta Braves (then known as the Boston Red Stockings) played five years in the National Association. They were the only one of the 10 original teams to play continuously during that time. In 1876 they then joined the National League in it’s inaugural year.
They had a pretty good first season in 1871. They won 20 out of 30 games. Unfortunately, they finished in second place. Philadelphia was two games ahead of them.
The good news is, they then won the pennant the next four years.
And …. they are still playing today. They are the Atlanta Braves.