Hello & welcome, I am Dr. B, a licensed veterinarian and I would like to help you with your wee one today.
I am very sorry to hear about this poor wee kitten. If she is not able to use her back legs at all nor feel when you pinch them, this does suggest spinal damage for her. If she could at least have felt your pinch, then we'd have other differentials (ie soft tissue injury, fractures, etc). But if she has no feeling in her legs, then this is a red flag there has been a spinal injury leading to swelling of the spinal cord or a bleed in the cord. In regards ***** ***** causes, the most common will be trauma of some nature (ie rough handling, being dropped, falling from a height etc). We can sometimes see spontaneous issues with vertebral discs pressing on the cord, but this is very rare in kittens. And while there are infectious agents that can affect the nervous system, we'd expect more kittens to be showing signs and brain based issues (affecting all limbs).
In this situation, keeping this little one safe from harm is the mainstay of treatment here. She should appear normal otherwise (eating, drinking, etc) but may not be able to urinate on her own. I wouldn't advise trying to express her bladder (since this is a delicate procedure and we'd not want to rupture her bladder by mistake) but just be aware that if she becomes dull, depressed, weak, collapsed, or vomits; this could be the cause of that and she need to be seen urgently. Otherwise, as long as she is stable she can wait until your vet can see her tonight. That said, if they confirm a loss of sensation and motor function for her back legs, her prognosis will be poor. They may be inclined to try her with steroids or feline safe anti-inflammatories to see if spinal inflammation is present but again loss of nervous function to the back legs carries a very guarded prognosis for this poor little one.
Please take care,