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I've been living with this issue for a couple of months on my 2003 MDX.

It has the Bose Stereo with Navi.
Everytime I turn on the car the two speakers on the front (doors) take like 5 min to start working. You can hear a BUZZZ for like a minute then they start sounding.

I did replaced the 2 speakers but still same issue.

Any ideas?

 

If you replaced the speaker and still have the issue, then it's more than likely to be the amp going bad. Trying replacing it with a known good one and see it that solves that issue.