Smith told reporters in Grenada on Sunday afternoon local time that he no longer has stitches in his previously fractured finger and has since had a smaller splint applied than the one he wore in the days immediately following the injury.
The 36-year-old spent the last week and a bit in his New York City (NYC) apartment, where he and his wife Dani Willis have lived since 2022, where his involvement in cricket was limited to a couple of 50-ball sessions in a nearby baseball batting cage.
Having complained of being "bored" and "stuck in the (hotel) room doing nothing", the former Test captain instead opted to take the four-and-a-half hour flight from Barbados to NYC to view Australia's first Test victory over the West Indies from the comfort of his American home, where he "watched pretty much the whole game".
"Good to see the boys get a win," Smith told reporters.
"It looked a pretty tricky surface to bat on. There were a few occasions I was pretty happy not to be out there with the things the ball was doing on that wicket.
"I thought the way the boys batted on the third morning - particularly Alex Carey - was exceptional. I sent him a message after that innings and it always looked like 300 was going to be too many (to chase) on that surface."
Smith returned to training once his medical team were able to apply a splint small enough to fit in his batting glove, and whilst he was not yet in a position to be able to confirm his imminent return for the second Test, his progress has been encouraging.
"I had a couple of bats last week with some tennis balls one day and then some cricket the balls the next day," Smith said.
"A mate found a batting cage (in NYC) under a bridge and he was able to throw me some balls. It was nice to hit a few balls. I videoed it, sent it back to the medical staff and they were pretty happy with some of the shots I played.
"Today I got stitches out and got a smaller splint so it will be easier to fit in the glove. It will just feel like training as normal now. I just have to get used to the slightly limited movement with the splint and the tape, but it's not too bad."
Should he return for Thursday's second Test, the 117-gamer won't be occupying his usual place in the slips cordon, where the injury occurred.
"I'll probably field some balls in front of the wicket, which will be the strangest feeling for me.
I don't think I've ever done that in a Test match. It'll be fielding at either mid-on or mid-off or fine leg. A bit different to standing at slip. It might not be so bad. I might get to do a bit of running around."