How it works
§ 12-1.3-2(f) allows a motion for expungement of records relating to a deferred sentence "upon its completion," expressly "without regard to subsections (a) through (c)" — which is where the first-offender requirement and the five-year wait live.
§ 12-19-19(c) supplies the mechanism: once the court determines after a hearing that you complied with all the terms and conditions of the deferral agreement, you "shall become immediately eligible for consideration for expungement."
What compliance means
Both § 12-19-19(c) and § 12-1.3-3(b)(1)(ii) spell it out: all the terms and conditions of the deferral agreement, "including, but not limited to, the payment in full of any court-ordered fines, fees, costs, assessments, and restitution to victims of crime."
The court must also find there are no criminal proceedings pending against you and that you have established good moral character.
The one absolute bar
§ 12-1.3-3(b)(1)(ii) ends with it: "no person who has been convicted of a crime of violence shall have their records relating to a deferred sentence expunged." That is a defined statutory list, and it is worth reading before assuming it covers your charge.
A note on the deferral period
Under § 12-19-19(a), when a Superior Court formally defers sentence, you and the court enter a written deferral agreement filed with the clerk, and the court may impose sentence only up to five years from the date of that agreement unless you are found to have violated its terms.