khafra could have easily assumed credit for the structure and built minor ones around it to ad to the complex.
Or, a restorer. Thutmoses IV restored the Sphinx and put up a stela to commemorate his work around 1400 BC. Were the sphinx there, 1,000 years earlier, it may well have needed 'restoration' as well and that would have been the time of Khafre (Cephren).
In any case, let me correct my earlier assertion. West speaks of First Dynasty mud brick tombs, not Fourth Dynasty. The error is mine but it actually serves to make the point even more valid.
In Serpent in the Sky by John Anthony West, in Appendix II he discusses his trip to Giza with Dr. Schoch. The tale about getting permission from the Egyptians was interesting as was Schoch's early findings but this passage turned out to be the clincher for Schoch.
We extended our inquiry into some of the pieces of corroboratory evidence I'd pieced together earlier but which needed geological expertise to back them up. In Saqqara, seven miles south of the Sphinx, there are mudbrick royal tombs dating from First Dynasty Egypt (ca. 3000 BC or five hundred years before Chephren's time.) The soft mudbricks are still in stable and recognizable condition. Was it possible that the limestone Sphinx could sustain three feet of weathering to its body, while a few miles away, the mud bricks in tombs supposedly older could still be used in construction today? Schoch thought not, and he was now willing to go on record that the Sphinx was older than dynastic Egypt.