From Battletech Modding Wiki
The following information was posted on REDDIT for the skipping of the tutorial missions.
Having done the tutorial a few times now, I find myself not wanting to do it again. So after digging around in the files I found a folder named "milestones" (\BATTLETECH\BattleTech_Data\StreamingAssets\data\milestones) that contains scripts for activating and organizing the story stuff.
Ok, so the part you're probably here for:
(Sidenote: any text editor will work fine, but I recommend Notepad++ since it's free, useful, and awesome)
Open the "milestone_003_title_coronation_palace.json" file and look for the section titled "Results" In that section you'll find "value" : 100, and change it to "value" : 105 (Don't lose your commas!)
Doing this makes it so that it'll play the first cinematic after character creation, then skip to "8 hours later" aboard the Leopard. (Skipping the tutorial missions 1 & 2)
Image, for those who need it.
If you want to skip the Majesty Metals mission as well, you also need to open up the "milestone_106_title_threeYearsLater.json" file, and go to the same section. But for this one, you change the "value" : 110, to "value" : 111.
If you try to skip directly to milestone 111, it'll break the game, since you acquire the Leopard at milestone 105.
I gave it a quick test, and didn't encounter any errors, but that doesn't mean there aren't any.
Edit: u/HatMadderer helpfully pointed out that you can skip directly to 114 (instead of 105, then 111), since the script for 114 also sets the variables to acquire the Leopard (With dev comments about it being for debug puropses) A quick test shows that it should work as well as the above method, albeit with less modifications.