Yes this is possible
Since the question is update, this solution can only gives you the embed url not the HLS url, check @JAL answer.
with the ressource search.list and the parameters:
* part: id
* channelId: UCURGpU4lj3dat246rysrWsw
* eventType: live
* type: video
Request :
GET https://www.googleapis.com/youtube/v3/search?part=snippet&channelId=UCURGpU4lj3dat246rysrWsw&eventType=live&type=video&key={YOUR_API_KEY}
Result:
"items": [
{
"kind": "youtube#searchResult",
"etag": "\"DsOZ7qVJA4mxdTxZeNzis6uE6ck/enc3-yCp8APGcoiU_KH-mSKr4Yo\"",
"id": {
"kind": "youtube#video",
"videoId": "WVZpCdHq3Qg"
}
},
Then get the videoID value WVZpCdHq3Qg for example and add the value to this url:
https://www.youtube.com/embed/ + videoID
https://www.youtube.com/watch?v= + videoID