Please don’t give up on your bunny just yet, you have only had him for a week!
I got my two bunnies as siblings more than a year ago. The smaller one, Myo, was very sweet and friendly from the beginning, but his brother Timbit was very aloof and wild rabbit like (ie nervous, running away when you approach him, etc). He even bit me once during the first month. However, about two or three months in he started to get much more comfortable with his surroundings and with me and the other animals in the house. Now (1 year later) he will come up to my dogs easily and let them sniff him and even just sit beside them. He will come up to me himself and circle around my feet and eat veggies/treats straight out of my hand. He doesn’t get spooked anymore when I or any of the other animals come up to him like he did before. He lets me pet him with no issues and will lay his head down and close his eyes. And he would never bite me again – of this I’m certain one hundred percent. But he still doesn’t like being picked up that much – I think most rabbits don’t – and he will always be a bit uptight and somewhat reserved – that’s just his personality. Each rabbit is its own rabbit, just like people. Some are more challenging than others. But the challenging ones also have their advantages. For example, Timbit’s brother, Myo, may be much more laid back and easygoing, but Timbit is the one with the looks – he looks like a stuffed toy rabbit – literally lol
I think your rabbit is just getting used to you and his surroundings. Imagine how nervous and scared he must be feeling right now in a new unfamiliar home. Just give him time. Time and love and attention. And as others have said, let him come up to you. Take care of him and love him and talk to him, but if you notice that he doesn’t like being picked up or runs away from you, just let him be. I’m certain that with time, your bunny will learn to trust and love you in his own way. And he will seek you out himself. Especially when he notices that you’re the one cleaning up after him and providing him with his hay, veggies, pellets, treats, toys, etc. Rabbits are very peculiar creatures, they don’t show their feelings like other pets do, it can take a lot of time for them to get used to you. Especially when you consider that they’re prey animals and are used to looking after themselves and not showing their vulnerable side. But once you gain their trust they will soon reveal their true personality and claim their spot and be just like any other pet or member of your family!