If deep work is going to be a realistic possibility in the modern "knowledge worker" office, leadership has to stand behind the idea.
I suggest in my book that employees interested in depth should discuss the topic with their boss. In more detail, during this respectful conversation you should try to accomplish the following:
Explain the concepts of deep and shallow work, noting, of course, that both are important. Ask what ratio of deep to shallow work hours you should be aiming for in your job. Then promise to measure and report back regularly. (Most bosses will be interested to gain these extra data points.) (Source)
A local office climate open to this idea goes a long way towards making this possible, but that climate would have to stand shoulder to shoulder to help communicate the importance of these values to constituents, stakeholders, and colleagues outside the immediate organization.
Deep Work would likely would tend to favor the Garden over the Stream. See The Garden and The Stream.