The Sulphurites made a near-enough perfect start to their 2022/23 League Two campaign, netting three times without reply as they comprehensively overcame a Robins side who are strongly fancied for promotion this term.
Yet, although Welch-Hayes and his new team-mates served up an extremely encouraging all-round display, the former Colchester United defender has insisted that he thinks Town can perform better.
"It's a great start," the 25-year-old told the Harrogate Advertiser.
"I think it was a good team performance, but I don't think we were even at our best. In some areas, we were a bit sloppy - myself included - but I think we managed the game well and worked together well as a team, so it is definitely something we can build on. But, like I said, there is a lot more to come than that.
"It's a good win and something that we can build on and I know it sounds like I'm repeating myself, but I don't feel like we were at our best. I think we just did the basics well, we were solid and we took our chances.
"A lot of teams will come here and think that they can just walk over us, which can go in our favour if they come here laid back. If they want to come here and be like that, then that's fine. We got a good result today and we'll keep building.
"There was confidence and focus [in the dressing room before the game]. The gaffer got us ready, we were well drilled, we'd gone through everything in training and I think we have got a really good group here, there's good togetherness. So if we keep working we can keep improving going forwards."
Welch-Hayes, who was deployed on the right of Town's back-three on his competitive debut for the club, was involved in two of Saturday's game's key moments.
It was his header from George Thomson's left-wing corner which set up Alex Pattison to smash home Harrogate's opening goal, shortly before half-time.
With their advantage doubled through Matty Daly, Welch-Hayes then gave away a spot-kick when he caught Jacob Wakeling inside the penalty area.
The combination of the post and Sulphurites custodian Pete Jameson would however keep Ben Gladwin's effort from 12 yards out of the home net, and Jack Muldoon applied a finishing touch to a fine team move to wrap up the points not long afterwards.
Reflecting on his own contribution to the contest, Welch-Hayes added: "I don't suppose it can really get much better than that, a 3-0 win, a clean-sheet and even an assist from the header.
"Some games I can get forwards a lot more. Saturday wasn't really a game I could get forward and step in as much. I had to defend a lot.
"It was a penalty if I'm honest. There was a bit of a scramble in the box and I just tried to toe it away. Their player has been quite clever to be honest, I can't even stop and he's put his leg over mine.
"So, it was a penalty, but I don't feel that there is that much I could really have done differently because if I don't try to get to the ball then he's in behind me and in on goal.
"But, I enjoyed it. It was my league debut here and the fans were class. Even my family came up, which was good, I haven't seen them for a while so it was nice to see them."
Town finished last season with the joint-second-worst defensive record in League Two, so to kick-off the new term with a clean-sheet against one of the division's strongest outfits on paper does at least bode well.
Saturday's defensive display certainly wasn't faultless, however Welch-Hayes felt that getting the basics right was key to them managing to shut Swindon out.
"I think the back-three did well. We were on the front foot and we read the play well," he continued.
"I think we've got a good bond already. It's only the first game of the season and we've still got a lot to work on, but we've just been listening to the gaffer and our assistant manager and just need to keep working on the things they tell us to do.
"It's important to do the simple stuff well. I think that sometimes you can over-complicate it and if we defend well as a tight group then I think we can have a good season."