You start falling as soon as steal ends, which is the same moment you start throwing levitate. Starting to cast a concentration spell instantly ends any other current concentration spell. levitate performs an action to initiate a non-zero time period. The fall is however instantaneous.
The rules of the PHB are not clear: quite to your DM
The rules on PHB compliance / basic rules state:
A high fall is one of the most common dangers for an adventurer. At the end of a fall, a creature suffers 1d6 blunt damage for 10 feet of fall, up to a maximum of 20d6. The creature lands on its belly, unless it avoids suffering damage from falling. (PHB, 183)
If you strictly adhere to PHB rules only, then there is no answer and the DM has to decide.
The fall is instantaneous according to the clarifications of XGE.
However, based on the clarifications provided in the preface to the optional rules on Xanathar's guide makes this rule much clearer by default.
the [PHB] Fall rule assumes that a creature immediately loses all distance when it falls. (XGE, 77)
Thus, using the default rules as specified by XGE, a creature has no opportunity to do anything once it begins to fall. They at once travel the distance and suffer the damage or other effects they triggered.
So as soon as you stop being touched by stealyou will fall the full distance before you can cast another spell or do anything else.
Note that the fly will stop as soon as you start throwing, because the concentration will end when you cast another concentration spell.