I am thinking it may be related to hot car, or something like a sensor, is getting too hot or starting to fail.
That's why I mentioned the "CKP" sensor, that one would not let the car CONTINUE to turn over, it would just drop and sit there, you'd try again and it would crank for that 3~5 seconds again, then dies ... nothing.
So you can crank the car, but no "fuel" - did you ever check the Spark Plugs for damage?
P0300 and P0301 are certainly misfires but is there an issue with the injectors?
Or do you have a failing harness?
Check the harness and the fuses back at the Fusebox, why? It's a 2013 sir, anything in the Electrical can generate a fault the system can not decode a code and throw a DTC over it when it is so intermittent