SInce when has Harley Davidson been manufacturing motorcycles?

Harley Davidson has been making motorbikes since 1903

That makes it 105 years since

Actually the boys started planning as early as 1901. They built a small engine and attached it to a bicycle in 1903. It was a failure. In 1904 they designed a much larger more powerful engine and a frame to hold it and created their first motorcycle.
All this information and a lot more can be found in "At The Creation" by Herbert Wagner