Have repeated this three times.
Going for a bike session I usually select the bike activity to get GPS lock and heart rate sensor at my house. But I do not press start, until I am out on the road. The house is at some 30 meters altitude, and the road starts after a small descent to some 20 meters, and some 200 meters away from the house. As I keep the activity in standby mode, I can see the altitude correctly reported, but when I press start, the altitude jumps to 595 meters.
The altitide curve during the session seems to be correct, but some 600 meters too high.
Will see if this happens whilst running too. I haven't noticed this until now, since I usually do not move between activating an activity and pressing start.