I have a similar problem (or maybe exactly the same)
You say that you starter just "clicks", mine actually activates and turns for a sub second and then stops, next try it starts just fine.
I ususally wait until the steering wheel has come fully up again before the second try, so that will be a couple of seconds too.
Sounds like the same problem, too much power for the battery to handle at that moment. Maybe the high amp stress from the first try gives it some more juice for the next, and thats why the second works.
Seen someting similar on my old -59 Ford Skyliner with a worn battery.
Time for a new battery?
2002 X5 4.4 with only 28 k miles on it.

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2002 X5 4.4i
1959 Ford Skyliner