How to change background to transparent

GMT,

I believe the image was made out of white paths with different opacities/transparencies on top of a black background, obviously as vector artwork.

Is the original artwork available, and can your equipment work with that?

If your equipment works with raster images, depending on the requirements, you can try to:

1) Place the PNG so it is contained within integer values of X and Y;

2) Create a black rectangle fitting the PNG and then Ctrl/Cmd+X+B (hold Ctrl/Cmd and pres first X then B) to bring it behind the PNG;

3) Select both PNG and rectangle, then in the Transparency panel Make (Opacity) Mask to create a negative version where the white/whitish parts become black/grey and the black part disappears;

4) Export as a PNG with transparency, maybe fitting the Artboard (also contained within integer values of X and Y) to the artwork.