Is it possible to stab an enemy before the hand goes into the ready position?

Solution 1:

Yes - whether or not the hand is in the ready position depends on whether your client thinks you're behind the target. Whether or not you get a backstab depends on whether the server thinks you're behind the target.

It's possible to get a normal stab even though it looked like you should have got a backstab, or to backstab when you think you're going to stab normally.

Solution 2:

From the wiki:

A Spy may backstab an enemy as long as the enemy is close within standard melee attack range, and the Spy is within a 180° range behind the enemy.

The important aspect is that the server believes the attack was executed within the appropriate range. You need not wait until the raised-hand animation completes (or even begins, for that matter).

Further down in the article you can read about the fine details of the attack (including the notorious facestab and a more precise definition of "within 180° range behind the enemy").