While the intro for Borderlands 3 is nice to watch the first time, it will get a bit boring if you want to try a different Vault Hunter. There are some good and some bad news; the bad news is that you cannot skip it on console. There is simply no way to do it, so it remains unskippable there. We can plead to Gearbox for them to patch in an option to skip it, and if they do, this guide will be updated to reflect that. Gearbox did indeed patch this in Borderlands 2 when it first launched, so it's entirely possible that they will do it for Borderlands 3 as well.
The good news is that you can skip the intro in Borderlands 3 if you play on PC. Here's how you do it:
Begin by going to the game files and head to "Borderlands3/OakGames/Content/Movies". Find the file called "MARCUS_INTRO" there and rename the file. Make the file name whatever you want to, but it's smart to rename it to something like "MARCUS_INTRO_BACKUP" just in case you want to turn on the intro again later. Now just save the renamed file, and the game won't be able to boot up the intro cinematic the next time you create a new Vault Hunter!
If you ever went to turn it on again, just rename the file back to "MARCUS_INTRO" and it will be able to load properly again.