Parker, if he gets the job, will be a bold and exciting pick. He's worked under several coordinators in a short time. Mike Pettine in 2019-2020, Fangio/Donatell in 2021, Ejiro Evero in 2022 and Vance Joseph in 2023. He must have had some good reviews for Fangio to hire him as DB coach in 2021 after only 2 years in the NFL.

His connection to the Packers was probably through Notre Dame. He coached there in 2017 and LaFleur coached there in 2014.

He had a role with the Broncos in 2023 that involved more than just coaching DB's:

So what kind of a coach is Parker and what would he run in Green Bay, if he were named the team’s defensive coordinator? There isn’t that much information about the 32-year-old who has yet to call plays at any level, but a few reports shed light on how well-regarded he is in Denver.

One of these comes from Taylor Kyles, a Patriots beat reporter, who had a conversation with Robby Davis, who covers the Broncos. According to Davis, Parker was key to transitioning the defense from the Fangio-style defense to the scheme that Joseph wanted to run in Denver. The Packers saw the mid-season improvement from the Broncos first-hand, as they were held to just 17 points only four games after Denver allowed 70 points to the Miami Dolphins in Week 3.
Vance Joseph speaks highly of him:

“He’s sharp, man,” current defensive coordinator Vance Joseph said of Parker on June 14. “He’s sharp. He’s a star. He is a great partner to work with. As a veteran coach, I’ve coordinated for about seven years now. My tape is out there, so I’m looking for ways to do different things.

“[I’ve been] speaking with Christian every day and bouncing ideas off him from what he’s done with Vic [Fangio] and guys in the past has been fun. [We’re] making changes and growing off what they did last year. He’s smart, he works his butt off and his players love playing for him. He’s a star.”