I'm thinking of crossing through someone's backyard without their permission.
Why do you want to cross through someone's lawn?
I want to go for a jog in the early dawn.
While it's good to be active, there are other routes for you to run on. Their private backyard is not the only place you can run through, and you shouldn't because it's illegal. You need to just suck it up and run somewhere else because the world is a wide place.
It's not that hard. I can just make a run for it.
I get that it doesn't seem like that big of a deal. But you should be really considerate of other people's property. Think of it this way, taking the extra time to walk around will add to your workout.