So, first I searched for availability on United but could not find any. Then I checked Air Canada Aeroplan, but I couldn't find anything there either. After that, I moved on to Singapore Airlines (they show availability within a range of +/- 3 days) and saw availability for only one specific day. The requirement was around 60K miles (I don't remember exactly, but it was certainly more than what Turkish offered), so I switched to Turkish Airlines.
On Turkish Airlines, I found the same availability. Since I was booking it for my sibling, I created a sibling's account on Turkish Airlines. However, I couldn't transfer miles from my account to my sibling's account, so I called them. The first representative said I couldn't book for someone else using my miles. I ended the call and called again, and this time the representative said yes, they would be able to book it. But in the middle of the process, their servers went down, so they said they would call me back after an hour to continue the booking. However, they never called, so I called them again to make the booking. Several representatives either couldn't see the availability or declined my request to book for someone else. Finally, I got connected to one representative who seemed knowledgeable and was able to complete the entire booking in 5 minutes.
I also learned that we can book tickets first and then have 48 or 72 hours to pay with miles. So, after receiving a confirmation, we can certainly transfer miles.