The Neolithic and Ancient Eras of humankind have the occasional Event that provide discount on the research costs of early technologies.  A handful of Ancient and Classical cultures even had discounts in their Legacy Trait for appropriate researches (Phoenicians at one time had a discoutn on sailing or fishing, the Romans on Imperial Power, and there may have been one or two others.

What about getting a discount to a military tech after fighting (and killing?) an enemy with weapons you don't have?  Fighting and killing a Gunner unit could give a 25% discount on Gunpowder Warfare, or more specifically fighting and killing a musketeer could give a discount on Flintlock.  You don't learn it automatically, just that by the time your empire is ready for that technology, they'll have had some exposure to it and can "catch up" more quickly.

I've suggested killing an enemy unit as a prerequisite to represent gaining access to defeated enemy's resources, but it could also be losing a fight against them and dealing with the curiosity and demand for information that such a defeat would lead to.

As an alternative, fighting against units of a technology you haven't unlocked could even fill the research gauge on that technology even if it's not something you've researched, so that after X+ fights or Y+ units defeated, you unlock the technology just through simple exposure, a sort of "wartime osmosis".