I've got the same "first thing in the morning" problem in my used X5 (also 2003 3.0i). It's OK in reverse out of the garage, but when I put it into drive it revs up a bit and then slams into gear. I've chirped the tires a few times when I've backed out onto the street and got on the gas to get out of the way of on-coming traffic. Mine also occasionally pauses and then shifts hard when going uphill, but only if I'm driving hard and on-and-off the gas.

I've alway thought it was related to low transmission fluid levels - torque converter filling up in the morning / uphill angles draining fluid from where it belongs. I was going to change the "lifetime fluid" next month until I read you did that to no avail. I've hesitated since the process requires you to do the final top off with the engine running. You can't even check it without getting under the running car.

I'm now looking for a VANOS or Electronic throttle adaptation issue. I've seen a few people post similar symptoms that turned out to be one of these.

I just reset my throttle adaptation and will post if that helps after I "retrain" it.