Engine shaking right after start and then fine

[klebmw]

Hi everyone,
My E70 2008 w/ 140K miles recently shows some issue. When i first start the engine, it's shaking for about 10 seconds and then running smooth. If the engine is running and then I stop and re-start it right away the engine is not shaking. It only happens when you stop engine longer than 15 minutes and restart.
I replaced ignition coil and spark plugs about a year ago and also replaced air filter and clean MAF sensor.
There is no engine check light.

I am thinking about the fuel pump pressure or fuel pump relay issue.

If it's related to fuel pressure issue, what should i replace? fuel pump?

Thank you all!