The 'object not found' error when pushing to GitHub is usually due to mismatches between your local and remote repositories. Begin by fetching the latest changes using `git fetch origin` and inspect any newly downloaded refs with `git log` or `git status`. Ensure your commits are correctly synced by running `git push --all` or `git push --tags` for branches and tags. In rare cases, this error can result from a corrupted .git directory, which can be fixed by cloning a fresh copy from GitHub, or replacing missing objects with `git fsck` and restoring integrity. This approach helps avoid future mismatches and keeps repositories aligned.