Paul would have been clean shaven right before having taken the vow of a Nazarite.
After this Paul stayed many days longer, and then took leave of the brethren and sailed for Syria, and with him Priscilla and Aq’uila. At Cen’chre-ae he cut his hair, for he had a vow. (Acts of the Apostles 18;18)
Nazarites would not cut their hair while under the vow but would have shaved clean just prior.
All the days of his vow of separation no razor shall come upon his head; until the time is completed for which he separates himself to the LORD, he shall be holy; he shall let the locks of hair of his head grow long. (Numbers 6:5)
Elisha was a Nazarite. His bald head was how the children identified him as a man of God, someone who had just taken the Nazarite vow.
***He went up from there to Bethel; and while he was going up on the way, some small boys came out of the city and jeered at him, saying, “Go up, you baldhead! Go up, you baldhead!” ***(2 Kings 2:23)
So yeah, at some point Paul was completely bald and clean shaven, just prior to taking the vow.
-Tim-