I'm looking for examples of startups that had no way of monetizing their original product, but then successfully did so after achieving huge growth.
The problem is that you said "monetize later" rather than "become profitable later".
For example, someone else suggested that Google was an example of a company that had no way of monetizing their original product. That's false. In the earliest days of Google it was obvious that there were tons and tons of ways to monetize the product -- hence the very early-stage investment -- though there was uncertainty of which ways of monetizing were best for growth and profit.
Echoing dasht's point above, no startup should plan to "monetize later". Plan for 'profitability later' but without some kind of test (like a sale) it's going to be harder to test and iterate on ideas (lean startup etc.)