If the aim is simply to mirror an existing directory, including mirroring suppression/deletions/new files/edits, and only copying what has changed (which is what I suspect you were trying to emulate with the "created after a certain date" thing), just do:
rsync -avh -P /path/to/source/ /path/to/destination
If the aim is to copy all files created since, say, three days ago, but not to update existing files or to remove files that have been removed from your source (which is what you described):
rsync -avh -P --ignore-existing --files-from=<(find -L /path/to/source -ctime -3 -exec basename {} \;) /path/to/source/ /path/to/destination
Edit: lemmy is html encoding my "lesser than" symbol in the second command above; replace accordingly
See here. Compatibility issues.