For some reason, using the channel ID that you obtain from sending the following get request:

curl -X GET "https://www.googleapis.com/youtube/v3/channels?part=id&forUsername={USERNAME}&key={API_KEY}" does not work when trying to find an active live broadcast for the channel.

Instead, I stumbled upon a roundabout way by using the "q=" parameter, which essentially searches for any YouTube video that contains the string in the "q=" parameter, to find the live stream via the name of the video live stream itself.

This is when I found out that the ChannelID that gets returned by this request is different from the ChannelID I got from the request above.

Using this channel ID I was able to get the video ID of a youtube live stream assuming that the channel was live.