As the prologue begins you find yourself on board a prisoner transport bus and the implication is that a crooked cop has found his comeuppance. That is a flash-forward...
Now we are back in the hear and now and you are yourself - the protagonist - who is a Miami Vice detective. You are with your partner, standing outside of the door to a flat you are about to raid, and you and your partner are exchanging witty banter and conversation.
In case you are curious, yes, this is the very same agency that Crocket and Tubbs worked for in the TV Show Miami Vice. In fact more than once you will catch the members of the Vice Squad making jokes that reference the show.
After you take the door you are prompted to place the first two suspects into custody... To do that you search and cuff them while your partner covers them. Actually you have to walk in front of your partner to do that which is really NOT the way that they really do it, but still...
After you cuff the second perp a woman bursts out of the bathroom and starts shooting! You end up in the middle of a firefight as the other two perps pull their weapons and pretty much everybody dies!
There is some evidence on the floor you need to grab, and then a new perp arrives, sees you and runs. You give chase, eventually ending up in your car pursuing the perp through traffic until your partner shoots out his tyres causing him to wreck. You then take him into custody and the POV changes to that of the news media coverage of the events.
When that resolves you are at the PD and your commanding officer is briefing you...
If you gathered the impression that the game is structured sort of like a TV show, well that is a pretty accurate impression, as it is presented is an episodic structure.
This completes the Prologue, unlocking the Achievement On the Job (20g) Complete the Prologue in Single Player.