Best time to buy alt coin is during pre ico stage because most of the ICO's provide 50% off during pre ico stage but risk will be maximum at this stage. It is possible that ICO may not be able to reach hard cap and finally they will not be able to list their token.

Another best time to buy on first day of exchange. I have seen usually price goes down at start due to huge selling events from bounty hunters. Buy some amount at that stage and wait for another dip. In this way you can earn more.