As the question is still active and you have stated that you wish to start off with a flat shape of the end model, I've varied @Scott Milner's suggestion and done as he has but using keyframed scaling instead. The inflation would be forward animation, not reversed.
The approach is to make the 'fully inflated' model you wish to end up with and scale that down in the Z axis ONLY to a flat plane and keyframe that at frame 1.
The plane is now your 'model' at frame 1.
Go to the end frame and scale the z axis ONLY, back up again, keyframe that.
You start with a flattened shape and end up with it rising to the desired model. I've done this here with the sphere and included the Blender file.
This has stemmed from @Scott Milner's answer so I'm not claiming any brownie points here.
The prepared answer follows -
Add the UV sphere (or finished model) and flatten it by scaling only in the Z axis to 0 to begin with.
Set a keyframe at frame 1 for scaling only.
Set the timeline cursor to the frame required. (say 50 or 60)
Rescale the flattened sphere back to it's original shape. i.e. in the Z axis only.
NOTE: (For newbies) you may not be able to scale it back up using the gismo arrows. Instead, open the Properties icon, the little cube at the right of screen. You'll see the scale slider when you open the "Transform" tab.
Place your cursor onto the Z axis slider and drag to the right. You'll see the figures scrolling up. The flattened model will begin to inflate upwards.
Keyframe that scaling setting. Leave the cursor in the Scale panel and press ' i '.
The circular plane will rise to the occasion and inflate back to a sphere.
Note that it's topmost section remains flat but it's no problem to use a Shapekey on the uppermost central vertice and have it rise a little to restore the fully spherical shape, which I've done here. (See Blend file)
Another problem can crop up, this one involving shading -
When the sphere is flat it's goes shadeless. At frame 2 where it begins to inflate, it switches to ordinary shading again, the transition far too annoying to ignore.
The solution is to go back to frame 1, get back into the Z scaling panel at right and tweak the Z scale ONLY from outright zero to 0.001 . Keyframe that.
(with the cursor still in the Scaling panel, press 'i') (see pic)
That fixes it . Shading starts normally and stays that way.