Gunpowder was fairly marginal as a weapon, except for sieges, up to the late 15th century- the Italian states (we agree the Renaissance started in Italy?) used mercenary forces of Swiss pikemen as their mainstay up till then. It was only in the 17th century that gunpowder really democratised death.

It was a term that was only used afterwards, when the effects were obvious, like the Industrial Revolution, so it's perfectly possible that it didn't have an origin, rather several streams that happened to flow fortuitously together. There had been revivals in learning, art, architecture, technology, and agriculture earlier- see Jean Gimpel's excellent book The Mediaeval Machine.

My own take involves the adoption of paper- becoming widespread by the 14th century; increasing complexity of society as landowners found it cheaper to pay people than to extract unwilling customary services, and to enter the market economy to a greater extent. Their needs were serviced by the merchant class, who both had money and needed to keep track of their trading. The more complex accounts thus required by both aristocracy and merchants lead to more widespread literacy (Chaucer, Piers Plowman, many others); this leading to a demand for reading matter, with the invention of printing (mid 15th century onwards) supplying the demand.

I think it was paper, printing and literacy that made it "The Renaissance" rather than a mere change in artistic style, and spread it among the population at large. This in turn led to the examination of social structures that brought about the Reformations.