1972 240z automatic transmission 3a71b

Anybody with technical knowledge of this transmission model? I need to know how to fix the following problem.

When cold, it shifts nice in first gear for the next 500 feet and after, there is no more power for three to five seconds. Its like the engine is disconnected from the transmission. I give some throttle and it engages back. When hot, this problem never happens and always shifts properly.

I check the oil level when hot and the engine idling and it is at the low level. With the engine shut the oil level is at full.

This problem happens when I turn at the corner of the street and I am wondering if it is not the pump that sucks air because of not having enough oil.

I have the technical book for the 3a71a and I dont want to rely on this information because it seems that it is not the same transmission.

There is no oil leak.