After May joined the Tigers mid-2025 with immediate impact, the club now needs to replace his power, speed and line-breaking ability for the opening rounds of the season.
They have turned to Jeral Skelton, the winger who was shifted to the centres when May was injured against the Cowboys.
May's absence may be more noticeable this week when Skelton has to match up against Rabbitohs veteran Jack Wighton.
"Obviously Taylan's a big part of this team on that right edge, but for us at the end of the day it's next man up mentality," Tigers captain Api Koroisau said.
Koroisau also praised May's resilience at training on Tuesday at Concord.
"I couldn't tell the difference (in May) today," he said. "He just bounces around, he's got great energy; he's always like that."
The injury came in an awkward tackle made by Murray Taulagi in the first half of the Tigers' huge 44-16 win on Saturday, which delighted the Leichhardt Oval faithful.
It was the joint venture's first opening game win in six years.
The Tigers have shown a few flashes of brilliance in recent years, occasionally dazzling crowds with a big win.
However, their problem has been maintaining that form, something that's still a question mark over the squad until they can prove otherwise.
Second-rower Alex Seyfarth believes attitudes are changing in Tigerland; a side previously chuffed with one victory now craves more.
"You probably could say in the past, we'd pat ourselves on the back after getting the win," Seyfarth said.
"We've got a whole heap of winners in this team ... so we've gone out today, we've forgotten about it and we're working hard for next week."
A winner of premierships with the Panthers and Rabbitohs, Koroisau echoed those sentiments.
"I feel like we have a new team, a new mentality,' he said. "Initially, it's all about consistency.
"We've got our standards of pre-season and those standards need to carry over into the season."
"For us, it's about being humble and staying consistent in our actions. That's the only thing that matters."
The forward-focused Tigers now turn their attention to their match against South Sydney on the Central Coast.
Koroisau admitted he was pleased former Souths teammate Alex Johnston broke the NRL's long-standing try-scoring record prior to Saturday's meeting, amid wild scenes in the Rabbitohs' loss to the Sydney Roosters last Friday.
"I think it was just incredible for the game of rugby league all together," Koroisau said.
"I'm glad he didn't break it against us - I would hate to be on that field - but it looked incredible."
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