I have been a cat owner for pretty much ALL of my life. And ALL of my cats have been 100% litter box trained. And....I hate to say this....I would NOT live with cats that weren't. So here is my advice.
1. Do you have friends who have cats that are litter box trained? Or a vet that keeps cats in the office (that are litter box trained)? Cats learn litter box stuff from other cats. And if your cat was rescued, and is ONLY 7 weeks, it probably didn't have enough time with mom to learn about the litter box. (BTW both of my cats were rescued, but I didn't get them until after 3 months old. During this time they were raised by a lady who had other litter box trained cats)
2. Although my cats are 100% litter box trained, I did go thru a 2 day period where my girl cat decided she didn't want to use her litter box (see story below). I talked to my vet about what to do and this is what she suggested. But UNSCENTED litter. Cats have a stroger scense of smell, so any perfume litter is REALLY offensive. If you buy the gravel, try the sand and vise versa.
3. My girl cat (who had NEVER had a problem with litter box) decided to STOP using her litter box for 2 days when I brought my newborn son home from the hospital. She decided my bed was her new bath room. She was obviously doing this on purpose. She always idd it in front of me. And my 5 year old cat was old enough to know better. And so this probably won't work for you....but I thought I would mention it anyway. After she did it, I picked her up by the scruff of her neck, yelled at her, and threw her in the garage (which she hates) for 2 hours or so. After doing that for 2 days, she learned. Your little kitten....probably doesn't know what she is "SUPPOSED" to do......but I thought I would mention this for future refferance.
4. Lastly, keep her in one room (as suggested below), with her food, litter box, water, and bed. Maybe being in such close proximatity to the litter box for a few days will help her get the idea.