Gulden, 22, is sidelined indefinitely after having surgery on a fractured ankle suffered when his leg got caught under him in a tackle during Friday's pre-season match against Gold Coast.
Sydney, who are missing skipper Callum Mills for at least their first three games, will now also head into their season opener against Hawthorn on Friday night without Gulden.
"Personally, it's obviously you go 'oh no' for a bit - not shy away from the fact he's one of the best players in the competition. It's a big hit for us," Hayward said on Monday.
"But it was a football injury. These things happen. We wrap our arms around him, and he's as professional as they come. He'll do everything he can to get back.
"But other than that, we can't change it. We've just got to get on with it.
"And we've got some really good young players and guys that are fighting for a spot that are ready to come in and play footy."
Hayward backed two-time All-Australian Gulden to still make his mark early in the season.
"I spoke to him on the way here, actually, this morning," Hayward said at the opening round launch.
"He's good. He's out of surgery. I think once that's all done, it's all sunk in now, he's in touch with reality.
"He's super-professional, so he's already turning his mind to what he can do to get back and and help the team.
"But he's a great leader of our football club as well. So he'll be having an impact without stepping on the field."
The Swans insist they have well and truly moved on from last year's horror grand final loss to Brisbane Lions.
"They're tough to get to, grand finals and it's not about going and doing it. We need to get there first and that starts on Friday night," Hayward said.
"So we're fully focused on that.
"The grand final's done and dusted. We move on."
Hayward insists a well-publicised vigorous review of that capitulation has Sydney well placed to do just that.
"The fact that we sat down as a group, spoke about it, reviewed it, that's not something we did so much with the Geelong one (in 2022)," he said.
"But we looked this one in the eyes, we learned a lot from it. And as soon as we did that, it was behind us.
"We're all still maturing as a group. All our young guys are now really experienced players, which can only help going forward.
"So I'm optimistic about what we can do this year."
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