How to grow baker's yeast (Saccharomyces cerevisiae) at home without creating a sourdough starter?

You can try it on agar. Or you could imitate the industrial method. The industry uses diluted molasses and aerates the solution - yeast needs oxygen to multiply, in anaerobic conditions it does not multiply but converts sugars into alcohol. You could also try to sterilize the flour (pressure cooker / oven).

Note: air contains wild yeast cells and lactic acid bacteria. So the chances that they contaminate your culture is high.

Also note: if the culture is not well aerated, it produces alcohol, which in turn attracts acetobacter, which turn the alcohol into acetic acid.

When culturing mushrooms, the growers try to make sure that the selected mushroom strain is the one, that colonizes the substrate first, because it can then outcompete moulds and bacteria. I think if you have a high yeast ratio, it might be able to outcompete lactobacilli. This way you could probably use flour without having to worry that it turns sour.

Edit: lactic acid bacteria likes anaerobic conditions, in the presence of O2 it forms H2O2 which limits its growth. This could also be used to improve your LAB/yeast ratio.