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I agree with you on few points still it's going to be interesting Uzbekistan is now one of the good sides in Asian region and things are clearly favouring them for having good results in future because they are having good skills and talented players.
Recently few players joined big clubs which give them good boost still need them to have good performance against top teams in the future, but their recent performance is not bad at all currently they are ranked 66th in FIFA rankings, but I am sure this is going to be improved with they are having strong structure which will help their youngsters for having good results. Difference of quality is huge but still with quality and consistent performance few teams can do much better which will give them confidence for big events like FIFA World Cup in the future.
Recently a few players joined big clubs? It's possible that I fully missed that of course, but which players are you talking about and what clubs are they playing for today? I am not aware of any player from Uzbekistan playing for a big club. Very few have made it to the European top leagues as far as I know and if they made it there, they didn't play for the best clubs. I am all ear to learn from you where those players are now at.
As for the World Cup, yes it maybe possible for them to get some improvements done and rank up a little due to good performances, but I don't think they will make it past the group stage. They are still far away from competing with normally strong teams at the World Cup.