There were no 3 tier A/C sleeper coaches back then. Before independence, there was only 1st class A/C, as they felt that only the 1st class passengers would prefer to spend money on A/C travel.
Deluxe (Poorva and Paschim) trains were the first trains to get A/C chair car to cater to second class and third class passengers. Shortly afterwards, A/C 2 tier sleeper too started.
Partly due to design issues (earlier A/C coaches used a different A/C system, which made it difficult to get uniform cooling in the coach, especially for the...
more... upper berths in sleeper coaches), 3-tier A/C coaches were not constructed initially. Once the design issues were resolved, production of 3 tier A/C sleepers commenced.