Short answer: Use time constraints as a launch pad to develop deeper understanding.
Longer: Using a very limited time to develop a deep understanding of something is setting yourself up for failure. Instead of trying to develop a deep understanding quickly, develop a broad understanding VERY fast, then use the remaining time to dig deep.
I try to develop an overview of the subject material as fast as possible. Index as you go, noting key elements and their sub-elements. Do not stop to read details! Aim to be able to describe your subject material/system in as few words as possible, but covering every aspect. Simplify!
When you finish this overview-index, time to analyze that data. Which elements are the key pillars of whatever system you're looking at? Which elements are you most familiar with or easily understand? What is the most un-intuitive?
Now that you've analyzed your overview-index, you should have a decent base understanding of the subject matter and what you're dealing with. You now also have a road-map to what to explore deeper as time permits.
Hope that helps.