Fuel pump relay issues are hit or miss. The car will either die or it will run fine, not much in between.

The engine temp sensor has a huge influence on cold starts. Measure the resistance -- it should read ~3500omhs cold and ~300-500omhs warm.

Next check all idle air hoses attached to the idle control valve for vacuum leaks. If they are hard and never been replaced, get them swapped out. Even a 1/2" crack will cause a no-start or very difficult to start condition.

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2016 Monsoon Gray Audi Allroad - 21k
2008 Black Mercedes E350 4Matic Sport - 131k
2014 Jeep Wranger Unlimited Sahara - 62k
2003 Gray Mercedes ML350 - 122k