In the real Scrum, your team understands the mindset and they are "living" Scrum. They take it as the way how to focus on customers, how to innovate, how to collaborate. The estimates, efficiency, and utilization become quite unimportant, as they focus on delivering value to the customer and overall long term results. The first step here is usually "Team Scrum" where the development team becomes a real self-organized and cross-functional team which works together. The team creation process produces a huge trust internally among the team members but also externally to the organization. It's the first tiny 'snowball' which afterward starts the whole transformation and creates forces to change how we run our business and how the organization itself is structured.
The "Organizational Scrum" builds on top of the values we experienced at team level – openness, transparency, and trust which leads the organization to be more business driven, flexible, and open to innovations. The business slowly starts to be picking up and the organization has to follow the rest. At this time, the snowball is big enough to attract the rest of the organization. At that time, you are truly Agile.
Such transformation can take years. It's not uncommon that companies are falling back and restarting the whole initiative again. It's hard. To succeed you need a good reason for change and courage. Eventually, every company has to change as the word is getting more complex and fast. The same way as industry revolution changed the way we were hundred years ago, the complexity of our current life is changing us now. To succeed in a long term, we have to be more flexible and dynamic – more Agile.