To fix audio out of sync in CapCut, separate the sound from the clip so it sits on its own track (the menu item is called Extract audio or Separate audio depending on your version), then drag that audio a few frames left or right until speech matches the lips, zooming in on the timeline for fine moves. If the project plays in sync but the exported video doesn’t, the cause is in the source footage or the export, and it is usually quicker to fix the finished file.
For a finished file, open the export in the tool above, press Detect automatically or line up a clap, nudge the sound in 10 ms or 1 ms steps and press Export video. The picture is copied as CapCut made it, so there is no second round of compression, and the corrected file is ready to post.