Good advice.
Also if you can check oil pressure, all through the engines working cycles (cold start up, warm, idle, high revs, load etc) and oil quality (should be ok if you service regularly)
Octane ping will only come into play under load, when accelerating, and truthfully it's almost a thing of the past with modern engine control systems. Nowadays, there's a knock sensor that detects preignition before you even hear it, and retards the timing until it goes away.
Well some pinging under initial load (ie low rev, high load taking off from the traffic lights) is still common even on modern engines that have smarter ECU's with knock sensors, especially on slightly older higher mileage vehicles, but those few pings are not much to worry about and it would have nothing to do with the start up rattle.
Rattling during start up is most usually caused by hydraulic lifters that have collapsed alittle until oil pressure (as Duke said).
Piston slap is another possible cause, but the slapping usually stops after the engine heats up and if it doesnt continues slapping all the time (but usually quieter), spun bearing can be another possible problem but really it would knock all the time and continue to get worse.
One other problem that can occur with some cars is timing chain rattle, usually
mainly due to hydraulic timing chain tensioners that when the engine is cold and oil is thick causing them to be alittle loose, it also maybe alittle slack all the time causing some rattle when on load from the traffic lights. I don't know what timing system the Taurus engine has though.
Most engine knocks/rattles are the result of low oil/oil pressure so thats the best place to check first.
We are all really giving educated guesses here as we cant check it first hand, as skip said there are a million things that could be causing it.