Not quite clear for me what you mean to say with "manually". A PSoC needs to run a program that (in your case) starts the ADC, starts conversion. What would you now do with the result of a conversion? You may do anything you like, but you have to write a program for that.
If you are thinking about triggering the ADC, you can keep it in continuous trigger mode or hardware trigger mode. In hardware trigger mode you can trigger the ADC externally. Also you can call ADC_StartConvert API to trigger the ADC once. So you can call this API inside an ISR to initiate one ADC sample conversion externally.