Even when time is tight, I don't recommend getting out of bed, lacing up the sneakers and heading right out the door for a run. When I start my run early in the morning, I always make sure I do something active before I run. Most days that means I'm walking my dog Sandy. It's not a super long walk (maybe 15-20 minutes or so), and it's not very rigorous, but a walk around the neighborhood wakes me up for the day, it gets my body moving, and helps prepare me much better for a long run.
I also recommend complete some sort of quick dynamic stretching routine before a run. Yeah, I know, when time is tight for folks who have jobs, kids, etc. it's hard to get yourself to stretch when you just want to get out and run, but you can complete a quick set of dynamic stretches in 5 minutes. When I was coaching my daughter's basketball team this year we completed a set of dynamic stretches at the beginning of every practice! Some easy dynamic stretches - toy soliders, butt kicks, and side steps. I can provide a more detailed dynamic stretching routine, feel free to reach out!
Warming up for a race is very different and as part of working with My Running Concierge, I will create a specific race day plan for each member of the MRC team, and that includes warmup.
To make it simple - before each run make sure you get the body moving for 10-15 minutes. This will help prevent injuries and help provide a better running experience for you!