You can't overcome this problem, its due to how the media is streamed. When you use media_play, the media has to be loaded from virtual memory and this of course takes some time, hence the delay. If you want to have an instant sound playing then use a pre-defined SOUND* object. This way the media source is already in memory.

If it seems more than just a simple delay, then it is probably a codec or hardware fault, not the engine.