This past week presented another new experience for Daniel Jones. He got into the Halloween spirit as Woody from the “Toy Story’’ movies as he and the other Giants rookies, in various colorful costumes, visited the Joseph M. Sanzari Children’s Hospital and the Children’s Cancer Institute at Hackensack University Medical Center.

Teammates and Giants fans on social media were taken with how much Jones actually resembled and filled the role of Woody — who, of course, is an animated character with an elongated face and aw-shucks earnestness.

This was another box to check off the daunting list of “firsts’’ for the anointed rookie quarterback. For the past six weeks, since he slid into the starting job after Eli Manning was benched, Jones has handled all the chores and assignments the role entails, such as meeting with the media two or three times a week. With the Giants on a four-game losing streak, these have taken on the feel of a question-and-answer interrogation.

“Yeah, I think I’m getting used to it,’’ Jones said, referring to the interview sessions, and not to losing.

At long last, and not a moment too soon, Jones can engage in something within the NFL that he has seen and done before, as the Giants face the Cowboys on Monday night at MetLife Stadium. Yes, this is Jones’ first career start against the Cowboys, but not his first appearance.

Manning played well and his defense played horridly Sept. 8 against the Cowboys at AT&T Stadium, and with the Giants down 35-17, Jones made his NFL debut with 1:46 remaining in what Marv Albert used to call “Gar-baaage time.’’

Jones completed three of four passes for 17 yards and lost a fumble after a 5-yard scramble. It was not much of anything, but leading up to that game Jones did study and prepare for the Cowboys, and he did get an ever-so-slight feel for their defense in his brief time on the field.

“Yeah, maybe just a little bit of experience against those guys,’’ Jones said. “I think just being able to watch that game, the second time we play them, the second time we’ll run our offense against what they do, it’s helpful to be able to see that and learn from it.’’

This is the first time for the second time around, and perhaps that will make a difference.

“Maybe a little bit,’’ offensive coordinator Mike Shula said. “More so than anything else, just getting his feet wet. But also, just recognizing the speed in person. These guys are really fast across the board. Up front, with the pass rush, with the guys, even if it’s man coverage, or their linebackers or their safeties, who are getting to the football fast. You see it on tape, but like you said, those few snaps, especially in that situation where we’re in throwing situations unfortunately for us, that might kind of help him recognize how fast they really are.’’

After taking care of business in the opener, the Cowboys rolled to easy victories over the bad Redskins and worse Dolphins, but then lost three straight before routing the Eagles a week ahead of their bye. At 4-3, no one is quite sure what to make of the Cowboys, but all the Giants know of them most recently is domination. Saquon Barkley is 0-3 against the Cowboys, and this will be the first time in his career he runs against an opposing defense for the fourth time, giving him something of a file on what to expect.

“You get familiar with them a little more than other teams,’’ Barkley said. “You just get familiar with your division more than other teams because you play them twice a year and other teams you may only see them once and you may not see them for another four years.’’

Giants fans are also more familiar with the Cowboys, and thus more sensitive to the lopsided nature of what this rivalry has devolved into. As the losing cycle spins, more and more Dallas fans fill the building, and the Meadowlands will be loud for both sides. The goal for the Giants is to make sure their fans stay until the bitter end and not allow a Cowboys takeover.

For more on the Giants, listen to the latest episode of the “Blue Rush” podcast: