Well, it kind of depends on what you define as teh first steam engines. Are you including like novelty stuff used for entertainment like magic shows and fountains? Or are we starting with the first steam engine used to do real mechanical work? The Newcomen engine came out in around 1712, but it's initial purpose as a water pump for mines wasn't really in direct competition to horse powered pumps. While they could be used to generate power for factories, that was an uncommon use case because they gradually lost power output over time.

The Watt design is when we finally saw steam engines replace animal power in the late 1770s. So not quite 100 years.

But yes, ICE development benefited from all the problems solved by steam power generation. I believe the ability to machine pistons to an accuracy of 0.1" wasn't developed until around 1750. Prior to that, people just hammered iron roundish and called it a day. Good enough for large steam engines, but not too valuable with an ICE.