Not always.Wouldn't the fact that the 2nd flush always is fine indicate that nothing is in the way?
Sometimes the trapway collects things that may catch and then not catch. It can be variable.
The main thing that has been mentioned above, is the same starting point in the bowl. The bowl water level should be at it's fullest before you try flushing.
If the water level has dropped in the bowl, then the first drop from the tank will need to replenish the bowl first, and then start the siphon. If you have things like pens or q-tips in the trapway, they can slow the siphon too.