Half Dome hike preparation water question

I was able to get a Half Dome permit and trying to plan for it. I am planning to park at the Curry Village parking lot and start around 6-7AM, maybe earlier. I plan to bring gloves, food, headlamp, and of course water. I also use electrolyte packets.

The main thing I am not sure about is where to get water. I usually hike with 4L of water but have been reading that I should bring 2L and use a filter to make the start easier. So I have the Sawyer Squeeze water filter with 2L bag, but it is not clear to me exactly where I should use the filter? Some people say there is a spigot and others say to fill at the river somewhere up the trail?

Any other tips would be appreciated.