Is there a way to mark a weapon as trash at the moment I pick it up?

Related: How do I mark an inventory item as trash?

I'm in the (very) early game, but I've got a couple guns that I really like. What this means is that I've got a LOT of guns that I immediately mark to sell as trash.

It would be super awesome if I could just pick these inferior guns up and throw them into a side pocket of my backpack, never to be looked at again.

Is there a shortcut to immediately mark a gun as trash at the moment I collect it, without going into the inventory menu?

Additional information: I'm playing on a PC and that's the platform I'm interested in, but solutions for consoles would be nice as well.

I don't think such a thing exists (ability to mark the weapon as you pick it up). But my system is pretty simple: I evaluate guns soon after picking them up - those I like get a star, those I don't get red X. Later, when I pick up more guns, I can easily find them because they aren't marked at all.