And it looks near perfect now. All smears are gone. Not a single grain of dust is visible. Great job! You put the lens cap on and a few hours later when you take it off you see - oh no!!! - grains of dust and fuzz is back. Even though you had the lens cap on all the time.
This could be because you have forgotten to clean something you might not have thought of - something I frequently forget and need to keep reminding myself: The inside of the lens cap.
Like myself you may not care a lot, where to store the lens cap while shooting. You are concentrating on getting the picture and taking on and off the lens cap is just a necessary annoyance as you still want to protect the lens' front element. In my case my lens cap typically wanders into my jeans' pockets. But even when the trousers come fresh out of the washing machine, the fabric is dissociating fuzz all the time. And very likely there is also quite some dust in the inside of the pockets from other things you put there previously.
Given the very uneven surface of a lens cap's inside fuzz and dust quickly accumulates in the edges of the inside of your lens cap. And the next time you snap it on your lens, and carry it around a bit, all the vibrations cause this dirt to fall on the front element of your lens.
So when you clean your lens never forget to clean the inside of your lens cap as well using a blower and a brush. And while on-the-go a courageous blow into the lens cap's inside using your mouth from time to time can help as well.