Perhaps there is another explanation for her not initiating a greeting when you arrive. I know with my T, she comes in to the waiting area and waits for me to notice her. She doesn't usually say my name or prompt me in any way, unless I'm completely oblivious to her. She does it for privacy's sake. The waiting area serves every business on the floor so there are often people waiting for a multitude of reasons. So, she comes in, smiles or waves at me, but doesn't say anything, and I get up and follow her out. Then, as we walk down the hallway, she usually walks in silence. She's giving me that time to order my thoughts, settle in to the therapy mindset, or initiate small talk, whatever I need to do.

Maybe your T is doing something similar when you arrive? Maybe if that's not what you need, you could try telling your T that you'd prefer she chat with you on the way to the office?