I don't know that your initial question was answered:
You can use the milk right from the cow to make cheese (although it is best if it was filtered first!) This is traditional and is what I prefer to do. I will often take milk from the previous night, skim the thickest cream off the top & save it for butter then warm it and add the warm milk from the morning's milking.
Traditionally, before refrigeration, the evening's milk was left to sit in a cooler place overnight. The cream would rise and the natural lactic bacteria would ripen the milk. Then that milk was skimmed (cream saved for butter) and the warm, morning milk was added. Since the evening milk was naturally cultured (from sitting for 12 hours over night), no culture was needed, just rennet, and cheesemaking would commence.
You can read some about this in Laura Ingalls Wilder's Little House in the Big Woods.
Happy cheese making!
Kristin