Modern fuel injected engines should normally start within one rotation of the crank shaft. When you first turn on the key (or hit the start button) the ECM turns on the fuel pump and pressurized the fuel system. Then as soon as the engine moves the crank and cam sensors tell the ECM which cylinder to inject fuel into and when to make the spark to ignite it. Again, most modern engine control systems do this very quickly, usually early in the first rotation of the crank. Of course to make this engine start so quickly there MUST be sufficient fuel pressure in the system for the injectors to work properly. To make this happen fuel injected cars do a fuel rail prime, a short fuel pump run when first powered up. The length of this run is only a few seconds (and on some vehicles that time can vary with outside temperatures, running longer when its cold out). After the prime the fuel pump will normally shut down until it sees a "running engine" (based on seeing a certain RPM) and then it turns back on. The funny thing is people will allow the engine to crank and crank like an old carburetor equipped engine. On an EFI engine this is not the way to do it!
You described a common problem, that is on a COLD start, that is the vehicle has been sitting for some time, the engine cranks for a excessive time. However, once you have run the vehicle and they you turn the engine off and start it again after only a short amount of time it fires right off. The most common cause of this is that the fuel pressure is slowly leaking down while the car sits. When you go to restart it after it has sat for a long time there is not enough fuel in the system yet to file in the cylinders. There is a quick and very simple test to verify this situation.
First try this: After the car has set for hours (long enough for the pressure to drop) get into the car. Turn the ignition fully on but do NOT start the engine. If you have a key its easy, just stop before hitting the "Start" position. If you have a push button start system just don't touch the brake pedal at all but push the button to turn the car fully on. (This requires two pushes of the button on most models). Once the car is "On" push the button again to turn it off and then repeat the process. Normally this will allow the fuel pump time to fully pressurize the fuel system to start the engine. Do this two or three times and then do a normal start. If the engine fires right off you know that its a lack of fuel pressure on start up causing your problem. Why does this happen? There are several possible causes. Some of the common ones are a bad one-way valve in the pump or a bad fuel pressure regulator, either of which will allow the high pressure fuel to leak back out of the fuel rail dropping pressure there. Another cause is leaking fuel injectors. This problem allows fuel to leak into the cylinders which can foul out spark plugs in extreme cases but will also cause the fuel pressure to drop too low for the next start up. (This problem will normally cause some black smoke to come out the exhaust as the engine is "rich" with all that extra fuel. Also the engine may exhibit a "miss" or stumble for a few seconds when it does start.
Of course there are other issues which can cause this, the ones listed above are just one of the more common problems and ones that are easy to check for at home. In a shop we would put a fuel pressure gauge on the fuel rail then observe what the pressure does when we shut down the engine. If we have a leak we will observe the pressure dropping off quickly or even slowly. This is the give-away. If the fuel pressure does not bleed off we need to look at other possible causes.
Hope that helps. Good luck with this. Oh, and BTW: I would test this first and if you do determine its a leak down of pressure, see your dealer. If need be have them compare your vehicle to other new vehicles as to cranking times. I know my 2017 just lights right off when I hit the button and it sits for a week or more more most of the time, sometimes several weeks, and it never has to crank over for more than a revolution. Same on my fuel injection motorcycle, it lights right off after sitting for a month or more.
