Huh. I would say the dream starts when Chu Shuzhi falls asleep/passes out on the steps of the Sky Pillar. Because he then "wakes up" at his desk at the SID in a scene that parallels the earlier scene in which Xiao Guo woke up from the dream where Lao Chu was strangling him, and is clearly very confused about how he even got to the SID. Then, there's nobody in the building except for him and (a lollipop-less) Zhao Yunlan, who a) doesn't yell at him for disobeying orders, b) doesn't immediately lose his shit on finding out that Shen Wei is chained, unconscious, to the Pillar Formerly Known as Ye Zun's Prison, and c) doesn't react to the news that Lao Chu sent Xiao Guo back to the SID earlier by saying he never showed up, let's go look for him. Then, there's the fact that Lao Chu even says he sent Xiao Guo back, with no apparent awareness it contradicts what actually happened; it's what he wishes had happened, just like it's his wish that Shen Wei isn't in danger and Zhao Yunlan isn't mad at him, and we only see things playing out that well-but-wrong in the dreams. It's stage one of the dream the Master of Nightmares needs to give him to masquerade as Xiao Guo and try to get Chu Shuzhi to sleepwalk out of Dixing and up to destroy the shield around the SID.

I don't think Lao Chu actually wakes up at the SID until the final waking, when I posit they probably found him collapsed in the vicinity of the building after resisting the Master of Nightmares. Or possibly he resisted breaking in and managed to just walk in on his own, but still asleep until the Master of Nightmares abandoned him as a failed ploy.