I see valid responses all over the board here from different contexts:

almost any absorbent cloth will do for direct pressure when you have EMTs and an ER in the near future. This includes home and auto accidents, SAR extractions etc. In fact in a pinch direct pressure without gauze or bandana will do, although really recommend gloving up first. Cloth can help with comfort for the patient with a bleeding wound you're pressing down on, and I believe it can promote clotting. FWIW I can't imagine not going in without some sort of cloth in my hand, my t-shirt even, and only rethink if the bleeding is excessive in which case I'm focusing on direct pressure or nearby pressure points to control bleeding. TQ is also an option then, though my gut is most bleeds will respond to pressure.

in WFA 24 hrs+ from the trail head and ERs and EMTs, they teach using gauze and direct pressure, and when one pad gets full put another pad on top (don't remove the soaked gauze, as some clotting may have occurred), and keep the pressure on, repeating as necessary. At a certain point there may be a decision to move to or supplement direct pressure with pressure points, or add or replace with a TQ but the most likely outcome is direct pressure reduces the bleeding sufficient to bandage up. You still work through your options in order - direct pressure, pressure points, then TQ if wound is on a limb. If you don't have an EMT or ER in the immediate future, control bleeding, irrigate wound, bandage, and continue wound care until you evacuate to medical assistance.