CoM takes place anywhere between a few days after KH1 to a month after KH1. They never really specify how long it is between the two.
This.
Plus, even if CoM were to start the same day as KH1 ended, it still fits in the timeline.
Why?
Because people say that Days takes place from the end of KH1, through CoM, and up until the beginning of KH2.
Which is close enough to the truth, but the story to Days starts with Roxas' birth, which was in KH1. Granted, it was at the very end, but it's still before the finish. Understand?
So during the time Sora's fighting Ansem's "Heartless" (I know, he's not a real Heartless, don't be picky, I just use that phrase to make it easy to understand.), Roxas may have met with the Organization.
So yes. Even if it took place the same day, it still fits.
Questions?