This sounds almost identical to my issue and it was just a fuel filter (my assumption is the fuel pressure regulator which is built into the fuel filter was leaking pressure) The only difference with mine is the car was only good for about 30 minutes. If I let it sit longer than that then it would have the start issue (but yes, start up just find on the second crank)

My pressure leak must have just been worst than yours.

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Matt Atkins
'01 Titanium Silver X5 4.4
'01 Lemans Blue M5