ESD and equalizing static charge of sensitive ICs before handling and soldering
Trust me, it is totally fine to dump it on to the ESD mat.  Think about what the antistatic bag does: it keeps any stray charge from going through the contents, but still can have a slight charge on its exterior.

So, if you are touching your mat with one hand and holding the open antistatic bag in the other hand, then there should be zero potential difference between the bag and the mat.  The are neutral to each other because they share a common ground - you.

Once they are neutral to each other, then the contents of the bag are also neutral and completely safe to dumb onto the mat.
Just make sure you are touching the mat with one hand and the bag with the other hand when you dump your stuff onto the mat.

I say all this as a person who is overly cautious of harmful static.