Crankshaft sensor

Just to confirm what you are saying, when you are using the key and turning it to the start position it cranks but finally starts after 15 cranks. When you push start it and pop the clutch, meaning you put it in gear and as it is rolling you let the clutch out with the key in the on position, it starts right away?

This is most likely due to a fuel issue. Either there is too much fuel in the engine when cranking or not enough. Let's start with checking the fuel pressure.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

If the pressure is ok, then it could be a crank sensor but it is unlikely because if the crank was the issue the PCM would not know when to fire the plugs and just popping the clutch would not change that. So this tells us that by popping the clutch the CKP sensor is okay. However, here is a video of changing it on a Focus which is the same vehicle as yours if you would still like to inspect or change it.

https://youtu.be/_xoGyRrHYbM

Let us know this info and we can go from there. Thanks