First week and I’m up a pound? Wth?

weight loss is not linear...if you changed up a workout routine you could have water retention; if you are eating more carbs that previously ditto; you could have increased cortisol in your body through stress and you'll see an increase

Starting exercise too?

Side effect of exercise is not weight loss but gain, water weight, for many reasons.

Are both weigh-ins valid to minimize known water weight fluctuations?
Morning after rest day eating normal sodium levels, not sore from last workout.

Are you a woman?
Anything less than a month is fraught with water weight changes.

Did you change your diet by merely leaving out some foods, or wholesale changes to totally different type of foods?
If massive changes, are you weighing all you eat?
Calories is per gram - weight, not by volume - cups and spoons.

And 1 lb fluctuation is nothing and easily possible for all the reasons above, besides normal anyway.
Have you ever weighed frequently enough to discover that fact?

For that reason then, more water won't like magically make retained water disappear.

The body is storing more water as a response to the exercise.
Just as body improves and breathing or HR slows down when doing the same workouts, so also storing more carbs with attached water, or increasing blood volume, or inflammation - all mean your exercise is doing as desired.

But there is a max to those kinds of improvements, once done body is happy doing your workouts with minor increases that wouldn't be noticeable probably.

At that point you'll start seeing the weight decrease along with the inches that has likely already been decreasing.
And frankly have many measurement stats, weight isn't the only nor the best one usually.