I run almost every day, I also just tread easily for a minute until my legs remember what they’re supposed to be doing and then slip into my normal pace.
I have tried warm up and warm down routines and have never noticed a difference, while I’ve noticed a huge difference adjusting my breathing, posture or pace while running, so I just don’t bother with warm-ups or stretches anymore, although if you’re looking for flexibility, I’m sure it would help to stretch after you run.