"Oh yeah, I'm playing!" Thibodeaux told ESPN after Saturday's final practice of the week.
It has been trending this way all week. Thibodeaux and fellow edge rusher Azeez Ojulari did significantly more in practice, even though they were listed as limited participants.
Ojulari, who had 8.0 sacks last year as a rookie, also expects to make his season debut on Monday night.
"I'm good," Ojulari said. "I'm excited, man. Ready to go. My first game."
Thibodeaux (knee) and Ojulari (calf) are officially listed as questionable, but they expect to play barring any last-minute setback.
"I hope so," coach Brian Daboll said before the final practice of the week.
Thibodeaux hasn't played since suffering a sprained MCL in his right knee from a cut block in the second preseason game against the Cincinnati Bengals. Ojulari was injured at practice this summer.
They were also limited at practice last week, but despite Thibodeaux expressing some optimism it always seemed like a longshot. This week they both took part in 1-on-1 pass-rushing drills and were seen not just jogging but sprinting.
"Improvement," Daboll said. "They've taken good steps. I think they are much better than they were the week before. Hopefully they'll have a good day [Saturday], and we're moving in the right direction with those guys."
Thibodeaux was the fifth overall pick in this year's draft out of the University of Oregon. He was having a strong summer prior to the injury.
There was little doubt that Thibodeaux was going to play a huge role in new coordinator Wink Martindale's defense. He had been a starter since the first day of OTAs in the spring.
The Giants (2-0) have played it cautiously with their edge rushers. They were doubtful on the final injury reports each of the first two weeks.
Thibodeaux felt there was something to prove this week.
"That I can go," he said. "I can be healthy, and I can perform the different moves and tasks that I need to do my job at a high level."
New York's defense has played well without its top two pass-rushers. They have allowed 36 points in the first two weeks. But they also have just three sacks.
Getting Thibodeaux and Ojulari back will be a boost for the defense.
"Explosion. Definitely pass rush," Ojulari said of what they'll be adding. "Hunting to the ball. Play as a unit and make impact plays together."
The Cowboys (1-1) are scheduled to start Cooper Rush at quarterback on Monday night against the Giants.