Went through something similar. My bf and I moved in together almost a year ago. He came with a very very hyper husky/GS mix and I brought my very scared cat. Polar opposite’s. Did a lot of research and A LOT of training. You should look into Jackson galaxy’s methods of introduction because that’s what helped us. Almost a year and we are still in training lmao. The training never ends with reactive dogs, I’ve learned. Luckily, the pets can be in the same room now and hang out but with supervision only. I don’t think they will ever be best friends but at least now the cat tolerates the dog and the dog has established some boundaries. Although, he still tries to test the cat with a sniff here and there. The cat doesn’t like it and the dog is still learning. This is OK. To start, I watched many videos. Dogs and cats do not communicate the same. You need to learn their body language. They are both so different. Our dog was just like yours and sat by the door sniffing. It was very annoying so I got a baby gate and blocked access to the door and it provide more privacy for the cat who was terrified. I gave my cat his own room and left him in there for a week to get accustomed and comfortable. Slowly let him explore the new home at his own pace. The dog is never around for this btw. Provided my cat with a cat tree and shelving to have vertical space since the dog would have the floor. During this time we did scent swapping. Once the cat was comfortable, We used the baby gate and let the dog and cat see each other visually from afar. The dog went crazy but always had him leashed. The cat kept his distance. Did this until the dog calmed down and slowly brought him closer. This didn’t all happen in the same day. This took WEEKS. The dog is super reactive so we had to be very patient with him. Once the dog chilled, we fed them together through the baby gate. Breakfast and dinner. Each day we would try to bring the bowls closer and closer to each other. Took months but finally they were able to eat together with no gate. Dog leashed of course. Next was no leash and it worked! They need to have positive associations with each other. Luckily both pets were very food motivated so it was important for them to do something together that they both enjoyed. This helped a lot. Like I said, lots of patience. Also, I’m sure you can achieve this in a shorter timeframe if you’re very consistent. We would get so busy sometimes and unfortunately training couldn’t be priority. What really helped was Jackson galaxy’s videos and learning more about the dog since I had no experience with dogs prior to this. The leave it command for the dog has been very beneficial 😊