What does Ivan do the first time he enters the exhibit?

Do you mean the mall exhibit or the zoo exhibit?When Ivan first sees the cage at the mall, he is relieved. He had been living with Mack at Mack's house since he was a baby. But as he grew, he found it hard to maneuver around Mack's place without disruption. Ivan says,

"When I saw my new domain, I was thrilled, and who wouldn't have been? It had no furniture to break. No glasses to smash. No toilets to drop Mack's keys into."

Ivan also says,

"I was relieved to have my own place."

He notes, in particular, that his "new domain" has its own tire swing.So, to Ivan, his cage at the mall is, at first, an improvement over his previous circumstances living with Mack. Ivan referred to that time as his "life as a human." Being at the zoo allows him to be more like a gorilla -- but not entirely.Later in the book, when Ivan is taken to the zoo by Maya, he spends some time alone in a cage, isolated from the main gorilla exhibit by a glass door. He watches the other gorillas, and they in turn observe him. He learns the name of one of the gorillas. She is Kinyani.When Maya opens the glass door, Ivan first spends time absorbing all the new sensory impressions the outdoor exhibit provides him:

"Sky.
Grass.
Tree.
Ant. 
Stick.
Bird. 
Dirt.
Cloud. 
Wind.
Flower.
Rock. 
Rain."

Soon after, he makes his first contact with the other gorilla residents. It does not go well. Kinyani chases him and throws a stick. He cowers and returns to his cage. He cannot remember how to properly interact with other gorillas at first, especially as a full-grown silverback male. His long-term social isolation at the mall has taken its toll.Ivan soon tries again, however, and the next day intimidates a juvenile male who is eyeing his food and then builds a nest for himself. This is his first step toward assimilating into the gorilla group.