Hello Budgiebird.
It was a good idea to adopt another pet. But it will take time, as Sophia16 has said.
When I got my cat she was a kitten,& that is way different from getting an adult cat. Mine was never a cuddle-up-to-you lap cat as I would have liked when I got her. & she never changed. 20 seconds was her maximum holding time. She would sleep at my feet,or at my side. & that was wonderful.
I grew to lo love other ways she behaved, loving her for who she was. Worrying all the time, too. Like having a child you have to be responsible for, keep safe, keep healthy, & not lose... it scared me so much. I still loved her.
I hope you can give your cat more time, watch, listen, be interested, encourage without trying to force more interactions. You might have places for your cat to lie upon where you can look up or over to see your cat while (for e.g.) at your computer.
My cat, Mekitty, had the windowsill, too. I knew Icould find her there most mornings. & if I went out, she'd often be there as well. I'd tap on the window, make my own meow noises, & she'd respond.
Generally cats are much more independent than dogs, who are social & need company more. They need more exercise too, more grooming, (though I did try to brush Mekitty sometimes when she let me), & they will more often seem to be paying attention to you.
Your relationship with your cat will be different. You can have a bond, but it may take you more time
In the end, you have to decide what is best for you, since the shelter has assured you they would take the cat back. If it's a good shelter, the cat will not suffer from being returned.
mmMekitty
