Trestman is not a head coach at the NFL level. That much is clear now. He's an OC. Doesn't have the knowledge or wherewithal to run a team in all phases.
Unfortunately, it's going to take a monumental collapse from this team to get him fired, IMO. I'm not sure even a 5-11 year would do it. Might have to lose all but 1 more game this year.
Knowing the Bears, they'll win 1 or 2 games at the end of the year to worsen their draft position, so instead of picking #5, they'll be like #12 or #13.