The vehicle can climb to an altitude of 90km (295,000ft), giving those onboard a few minutes of weightlessness and a view of the curvature of the Earth.
Sir Richard's intention is to introduce a commercial spaceflight service.
Some 600 individuals have already lodged deposits to take the ride.
Witnessing the British entrepreneur do it means those customers are now getting extremely close to having to hand over the full ticket price, which in some cases will be $250,000 (£180,000).
Sir Richard Branson said: "I truly believe that space belongs to all of us. After 17 years of research, engineering and innovation, the new commercial space industry is poised to open the Universe to humankind and change the world for good.
"It's one thing to have a dream of making space more accessible to all; it's another for an incredible team to collectively turn that dream into reality."
Absolutely key to Virgin Galactic moving forward with its business was the granting last week of a commercial spaceflight licence by the Federal Aviation Administration.
Sunday 11 July is the opening of what's termed a flight "window". The Galactic team will aim to make the ascent on that day, but it could of course be delayed because of unfavourable weather conditions or perhaps a technical issue.