It is a general observation that the best time to enter a GD is either at the beginning or the end. But, this may leave you feeling left out from the soul of the discussion. Therefore if possible, after you initiate the conversation, allow people to dive in and then formulate your replies on the basis of that.
Discussions seesaw regularly from an intense phase to a point of silence, its best to cover up these lulls and fill the gaps. Mostly in GDs, there are highs and lows which we call crests and troughs of the discussion. The crest is the high-intensity time period, generally when the noise levels are at their peaks. The troughs are the times when it is very little or absolutely nothing cooking up in the discussion. So, an ideal situation is the one when you see people drawing themselves back from the discussion for any reason, it is, therefore, important to prevent the discussion reaching a point of complete silence or the period of troughs. In competitive discussions though, crests will occur more often than troughs which will be very rare.
In such cases, wait for your chance and identify the perfect timing to hop in, probably during times when topics which you can relate to and have knowledge about are being discussed, here you can join the discussion irrespective of the noise level.