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Try lubing the front suspension bushings. My 90 LS creaked and groaned when I hit a speed bump and some lube eliminated the noise.
I have this same problem in Canada and I don't get overly much travel so I don't think my suspension is too worn yet.
It just started happening this winter and now with the warmer spring temps it still does it ONLY when the car is first driven from cold, I'm sure my scenario is the exact same as yours having said that so which bushings did you lube? Thanks.