The short answer is that the longbow was there before the English. It's a very old invention, and has been around for over 10,000 years (or over 6,000 years, depending on exactly how you define "longbow").

The longbow became more prominent in English armies when English armies professionalised, transforming from soldiers performing feudal service to soldiers serving for pay. The longbow was in English armies before that change, but it was present in larger numbers after that change. For example, Edward III's army at Crecy was approximately half archers, up from perhaps 25% in Edward I's armies.

When and how quickly? Edward I's wars in Wales and Scotland laid the foundation, and by Crecy, the longbow was successfully playing a major role.

For the longer version of this point, in answer to a question about the Welshness of the Welsh/English longbow, see https://www.reddit.com/r/AskHistorians/comments/9uccx0/what_was_the_origin_of_the_longbow/

To be able to successfully use armies with the longbow as such a major component, you need the right tactics. Specifically, you need to protect the archers, using field fortifications, armoured infantry, and/or cavalry. You need to integrate the archers into a combined arms force. You also need enough skilled archers, and incentive for them to serve as soldiers (e.g., attractive pay). This isn't a easy combination to just wish into existence, which is what makes the English use unusual - it wasn't something that everybody did. For the long version of this, see https://www.reddit.com/r/AskHistorians/comments/88zd54/the_english_longbow_seems_so_simple_in_its_design/

For further reading, Matthew Strickland and Robert Hardy, The Great Warbow: From Hastings to the Mary Rose, Sutton, 2005.