Question about Dana K. White's no-mess decluttering method

I've been experimenting with following Dana K. White's no-mess method and I really like that I can walk away at any point without having made a bigger mess.

My question is: how do you go about doing this for a literal container (like a plastic bin) that is overfull? I feel like I need to pull things out to even see what's in there. Do you just rummage around pulling out obvious things until you've created enough space inside the bin? When I write it out, that seems like the answer, but when I go to do it I feel overwhelmed working within such a cramped space. And it doesn't help that some of what's in there is in those vacuum bags, so I actually have even less space to work with.

ETA: thanks for all of your ideas and tips so far. I should clarify a few things: the bins are not random clutter/doom boxes. They all contain fabric or clothing to be repurposed as fabric, already sorted by category. They are transparent and have a high visibility home in my sewing studio. They’re accumulating clutter around them because I’ve been piling relevant fabric beside them because the bins are too full. I need to get rid of a bunch of fabric, clearly, or get rid of something else to have more room for fabric.