How to create a SVG that only has one color and transparent background with B&W image tracing?

To further try to explain what I mean, let me upload two SVG files. One of them is like how I want it to be(transparent background, the # color easily editable in it's code and there's only one color fill to edit) and the other is that Illustrator creates, at least by the methods that I tried so far, and is a mess to try to edit the color from the code and has a white background, which can't be removed without rasterizing it, which inevitably causes some loss in quality when you re-trace it.

In the "SVG-proper.svg", you can see that it starts with a

<g transform="translate(0.000000,1800.000000) scale(0.100000,-0.100000)"
fill="#000000" stroke="none">

and editing that #000000 will give you any color you want, in all of the document, no matter how complex it is, and there will always be a blank-null background, rather than a white one.

However in the image traced SVG of the Adobe Illustrator, which is "SVG-Illustrator.svg", you can see that it starts with a

<style>
      .cls-1 {
        fill: #fff;
      }

and the #fff is just the white background. There is no option to change the color of the vector at all. So let me be very clear with my question to leave no room for ambiguity, is it possible to create a style of SVG(from black and white image tracing) in Illustrator, that has the format of "SVG-proper.svg"? If so, how?