1) Compartmentalizing of biological functions. Its why a cell is a fundamental unit of life, and why organelles enable more complex life. Things are physically in closer proximity and in higher concentrations where needed.
2) Multienzyme complexes. Multiple reactions in a pathway have their catalysts physically colocated to allow efficient passing of intermediate compounds from one step to the next.
https://www.tuscany-diet.net/2019/08/16/multienzyme-complexe...
3) Random chance. Stuff jiggles around and bumps into other stuff. Up until a point, higher temperature mean more bumping around meaning these reactions happen faster, and the more opportunities you can have for these components fly together in the right orientation, the more life stuff can happen more quicky. There's a reason the bread dough that apparently everyone is making now will rise faster after yeast is added if the dough is left at room temp versus allowed to do a cold rinse in the fridge. There are just less opportunities for things to fly together the right way at a lower temperature.
3a) For the ultra complex protein binding to the DNA, how those often work in reality is that they bind sort of randomly and scan along the dna for a bit until they find what they're looking or fall off. Other proteins sometimes interact with other proteins that are bound to the DNA first which act as recruiters telling the protein where to land.