Won't the sunscreen come off a bit if I use a brush when applying base?

You have to use a brush to get a thin base, right?

But I get blemishes easily

Since it's skin, I have to apply sunscreen properly...

I usually apply sunscreen before base makeup, but since this is a moisturizing type, if I apply it with a brush after BB cream or foundation, wouldn't the sunscreen I applied beforehand get wiped off a bit in the direction the brush strokes?

I want to use a brush

I end up using only a puff because I'm worried the sun protection might drop for no reason.