at that time or that time
Here: When we say “At that time…” we often continue the sentence with details about what was happening generally during that period. When we say “That time…” we continue the sentence by saying what happened specifically and ONLY at that particular time. Sounds complicated but it isn’t:
Examples:
“I lived in London in the 1930s. At that time, most people were quite happy but there was a lot of talk about the possibility of war”.
“My mother was a secretary in Tokyo. At that time, it was still unusual to see women in the workplace”.
Versus:
“I kept shooting until I had no more bullets. I looked up and nobody was there. That time I made my decision to run away”.
“I used to go to France for my holiday every summer until 1939. That time, I couldn’t go because the war had broken out”.