Audio out of sync in Final Cut Pro

What do the original files show up as in a media app such as VLC? Does this info match what Final Cut says about the ProRes copy? The video frame rate, audio sample rate, and other information should match exactly. Then, your FCP sequence settings should be identical.

Another way to address small sync drifts is to razor-cut the audio and manually re-establish sync a few times on the project.

I had the same problem. It seems to be a ProRes issue. I fixed it by converting the audio to AIFF (ffmpeg -i video.mp4 -vn audio.aiff) and importing the new audio file into FCPX separately, then creating a compound clip with the video and audio.