Is there any difference between "at that time" and just "that time"?
Answer from a Native speaker
Yes, there is a slight difference! "At that time" means a specific moment in time. It's similar to "at that point." As an introductory phrase, it means at that point, period, or stage in one's life. Whereas "that time" means that general occasion or period of time that something took place. Ex: I didn't go camping that time in June. I went the next time, which was a couple of months later. Ex: It was raining at the time of the race. => the specific start time and duration of the race. = It was raining that time at the race. => at the one race this person to, it was raining. Opposed to all the other races they went to. Ex: At that time, I had no idea I was going to have a career as an artist. => point in one's life.