The Church does not teach that everyone goes through purgatory. Neither does the Church teach that the stay in purgatory is measurable in units of time, as the purgatorial cleansing occurs outside of time. So it was entirely possible for the Good Thief to go through purgatory and yet arrive in heaven on the same day.
It is also possible that he was ready for heaven as he died. Remember that he did everything a good Catohlic death requires: he repented of his sin, suffered for it in lifetime, did the work of mercy by defending the innocent, and asked Christ to save him. He died a good death; may we all be so lucky.
Regarding “faith alone”, where’s the chapter and verse on that? I can show you chapter end verse on the exact opposite, “not by faith alone”, James 2:24, in context.
Ephesians 2:8-9, “For it is by grace you have been saved, through faith—and this not from yourselves, it is the gift of God—not by works, so that no one can boast.”