You'll get a better understanding of the game from just playing if you've completed the basic puzzles. The advanced puzzles don't teach a ton about how to play the game, they're more just fun puzzles. And they're hard, even if you've played for a couple weeks.
Besides, there's plenty of time in between orders to keep working on the puzzles. The game moves slow enough it's easy to figure out. And the time machine lets you experiment and try out "what-if" scenarios.