Don't worry about the rain. There's no waiting around gameplay for weather changes. They are positional and cover a certain amount of ground, not time based iirc. If it rains it's just supposed to be an obstacle on your path. Also rain = BTs, so where there are BTs on your path there is rain.
Also worth pointing out that later in the game
spoiler (click to show/hide)
you will develop the ability to build timeshelters, which not only protect you from the effects of the rain, but also repair damaged packages and allow you to skip time to wait for the rain to pass.
