After being elevated from the practice squad for a third time, Smyth is now on the brink of earning a permanent spot on the Saints' 53-man roster.
NFL rules state a player cannot return to the practice squad for a fourth time in a season, so if Smyth is to play against the New York Jets on Sunday (18:00 GMT) he would have to be elevated to the senior roster on a full-time contract.
While his promotion has not yet been confirmed by the Saints, he says "things are looking good", a remarkable achievement for someone who in 2023 was still playing a different sport altogether.
Smyth is a former goalkeeper in Gaelic football in his native County Down and found a route into the NFL after coming through the International Player Pathway.
After joining the Saints in March 2024, he had to wait for his time to shine but made his regular-season debut last month after previous kicker Blake Grupe, now of the Indianapolis Colts, was waived and Smyth won a kicking competition with veteran Cade York.
"There has been a lot of work behind the scenes over the past two years, where you are maybe questioning if you will see the field, or if my lack of experience would hold me back," the Mayobridge native admitted.
"I was seeing too much progress to even think about coming home.
"I was wondering if it was ever going to come, especially with my experience and not playing college football, but I think I've shown people in this organisation, and they've shown enough belief in me, to go out and get it."