Some notes on training, based on my own BJJ experience:
We can probably assume the Cobra Kai's had been training in kids' classes for years, probably 3 days a week. They probably only recently went to 'adult' classes (ie in this case, it was all older teens), with an instructor teaching them how to fight tournament style. They would keep their own kid belts and get promoted upward from there, so not as long to get a black belt.
Daniel learned from someone who had him training every day, many hours a day. I'm making a rough estimate that Daniel was training 25-30 hours a week, for six weeks. Outside of Crane Technique which he taught himself, all of the karate that Daniel learned was functional. First blocking (which was driven into him with muscle memory from chores), then strikes (stupid amounts of practice).
Once Daniel got used to fighting on a mat, he did OK. He made mistakes. His opponents, although 'black belts', were teen black belts, which isn't the same in terms of testing and ranking (Kreese was rough but crippling his own students in classes means that he doesn't get paid by rich parents). The karate he learned wasn't point-based, so lots of the gimmicks for scoring points wouldn't work on him; I imagine Mr. Miyagi but the boots to him in the 'unreleased scenes' so he got really good at blocking and avoiding. Daniel was also a soccer player, so his cardio and physicality is already good. He caught Johnny with a punch off guard and hurt him in the beginning, so he already had a foundation.