I just wanted some advice and make sure I'm on the right track

So I got a kitten, Tilly, a week ago and I've been keeping her in the back room for the time. My resident cat, Pumpkin, used to hiss at the door when she heard her meowing but now she just ignores it. Pumpkin also use to hide under the bed and go out more than normal but she's not really doing that anymore. I've put a few of Tilly's toys and a blanket she slept on in Pumpkin's area and she just sniffs them and ignores them.
They have seen each other but it was by accident- Tilly was at the door when I went in and Pumpkin could see her. Pumpkin didn't really react. Is this a good sign??
Right now Tilly is playing in the back room and Pumpkin is chilling next to me. So I think Pumpkin is pretty relaxed.
I'm wondering how to go about introducing them face to face? I've got a cage that's pretty big for a kitten to put Tilly in with some toys and food but thing is she doesn't like it and meows a lot when she's in there. Pumpkin is a quiet little cat so she won't go up to Tilly if she's making a racket! I don't want to push Pumpkin into meeting Tilly but I can't leave Tilly in the cage until Pumpkin decides she'll have a little nose because it'll be hours!
Any suggestions on how to make Pumpkin more relaxed with the meeting?
Do you think Tilly in the cage in the living room, which is part of Pumpkin's area is a good idea? She'll probably just go out lol. Does that matter?
I'll be so grateful for advice!! thank you
