Hi Denise, and welcome! What generation is your boy? (Higher generation Savannahs--F1-F3--can take longer to acclimate). How long ago did you get him, and did you try quarantining him to one room when he first arrived? If he is free in the entire house, I would suggest containing him somehow to a separate room that you can spend one on one time with him, so he may bond with you and come out of his shell....that room ideally should be one that has his litter box, food dishes, cat trees or other high object he can climb on to feel safe. A large bathroom or bedroom or office is ideal. Spend quiet time with him and do not force interaction on his part. Read out loud so he can get used to your voice. Use a wand toy to see if he will respond, and fill his food bowl when you come so he associates you with good things. This may take some time; and you are correct that he will advance on his own terms. This is not something that can be rushed. It may take a few weeks, or months...remember that as an young adult this is very new to him: a new house, you, a new dog....take your time, and I am glad you are here! I'm sure others who have been down this road will chime in with more detailed advice.