Hi,
The player/device will download the chunks at the fastest rate it can with the bandwidth it has available. To speed up this process you can reduce the size of the chunks that the player/device is downloading.
By default the chunks are 10 seconds in duration and the player/device requires 3 chunks which is 30 seconds of stream before playing the first chunk.
You can adjust this using the Apple HLS (cupertino) packetization article
To check if the stream is smooth you can play it using VLC player or an Apple iOS device. If the client does not have the bandwidth required to play the stream then it will not play smoothly. To accommodate clients with lower bandwidth you can provide the stream in multiple bitrates and use adaptive bitrate (ABR) streaming which means the client will play the highest bandwidth stream out of the ones available and a lower bitrate if required.
Please see the article below for ABR streaming.
How to do adaptive bitrate streaming
Jason