Impossible? It certainly isn't impossible. From your perspective it could be called time consuming or something like that. What if some quest gave 10k exp? There's no mention anywhere how much exp a quest should give.
But there are no quests for 10 k exp (and if they will this is still nothing), and I don't think devs will make this.
Experience should be gained from various things, from playing the game, exploring and adventuring, not grinding.
This is true of course, but to gain 21 lvl from different things, you need to tag -
a) some kind of guns - don't have to talk about this one
b) you said crafting is not for exp, so at your point let's say we tag first aid and outdoorsman - there is some exp from those - but exping on outdoorsman is good for first levels, later amounts of exp is too small. First aid - same. I don't even mention that from crafting then it will be more exp, but here appears another problem, which I wrote here:
Crafting - it's also too nerfed and near to imposible to get 21 lvl by this, but besides this - let's say that after looong long boring time you will get this 21 lvl by crafting. To achieve this you must tag some kind of guns (bir or small or energy), and you MUST tag science and repair, cause to craft most-giving-exp things you need high science and repair. It means, all other skills would be useless, such as First aid, Doctor Sneak and many others. Another thing is - what if I want to do some silly warrior, which can't repair, but he is great in fight? He won't get a chance to have 21 lvl?