First, immediately stop the activity of rubbing his face in it. This is completely counterproductive, the kitten is not going to make that association, and is going to see this as abusive and become fearful of you. That advice is brutally bad, it boggles the mind.
Second, 6 weeks is way too early to separate a kitten from the mother, 8 weeks is minimum, 12 is best. So, whoever sold it to really has no business doing this and my guess is that they had an unexpected litter and were trying to get rid of them. That's unfortunate, a couple of more weeks and you might not be having this issue.
So, if you understand that the kitten is not properly weaned from the mother and trained by her, then you need to substitute for her. Some initial steps you need to do are:
Observe the pattern of elimination:
- Does he go in the same place? If so, put a litter box there.
- Does he always avoid the litter? Have you looked at a different litter option? There are some designed to attract cats for this purpose.
- Does he go beside the box or entirely away from it? If beside it, the litter or the box may be the issue. Any idea what litter the people that sold you the cat use?
- Does he spread it about? If so, he may be marking territory. Seems a little young, yet, for that, but still.
There's a whole program of behavioural medicine work around the answers to those questions, so a bit out of scope here. However, you can use this information to talk with your vet or use as the basis for trying some things out.
Reasons cats usually don't use the litter box:
- Prefers or dislikes a certain kind of litter (gravel may hurt his paws for example)
- Doesn't like the location, do you keep the litter box near his food? We don't like to eat in our bathrooms either
- Do you clean it frequently, cats are fussy and will avoid soiled boxes
- Fear, bad association around the current location of the litter box (which isn't helped by the existing bad advice you've already gotten)
Things to help:
- Keep the litter box clean (assuming he's using it)
- Wash it out once a week to remove odors
- Different types of litters, switch them up and see if he shows a preference
- Litter attractant, basically designed to attract cats to the litter box
- Check the height of the box, he may be having a hard time getting in it as a kitten and so avoids (if he's going beside it, this is a possibility).
- Don't put a lid on the box if you have one (concentrates the odors)
- Ensure you thoroughly clean the area he defecated on, preferably with a cleanser designed for this
- Move the box to a more open area and away from any food
- If he tends to use quiet areas, move the box to a quiet area. If he tends to busy, move to a busy area
Things to avoid:
- Liners, some evidence that they reduce litter box usage
- Punishment. This will make it worse, not better, and may alienate the cat
The things about punishment, and why I'm kind of harping on it, is that there's this idea that the cat should be able to grasp "bad" in this context. Get past the idea that cat is like a human, they don't see it this way, they're just pooping.