How to care for a scared cat?

This diwali, I found an unexpected guest on my roof ! A small 6 month old cat which nested itself inside a small closed space inside a staircase. My roof has a small 3 feet split so the staircase leading to the upper portion is where the cat made herself home.

Now the thing is, it looks dehydrated and visibly scared after diwali but it is not coming out to drink either water or milk. I think it's mum is still around and she's feeding her, though obviously not properly. Now, I haven't seen its mum but it's my best guess as there were some food scrapes littered around the opening. In this scenario, do I forcibly take out the kitten and take it to the vet or leave her as is? What else can I give her as food? I had also tried to give her boiled eggs but she just wouldn't come out and I don't want to scare her. (If i take it to the vet, i might cause stress to both the kitten and the mum)