You can use ImageMagick without separating the first page of the PDF with other tools. Just do
convert -density 288 cover.pdf[0] -resize 25% cover.png
Here I increase the nominal density by 400% (72*4=288) and then resize by 1/4 (25%). This gives a much better quality for the resulting png.
However, if the PDF is CMYK, PNG does not support that. It would need to be converted to sRGB, especially if it has transparency, since Ghostscript cannot handle CMYK with alpha.
convert -density 288 -colorspace sRGB -resize 25% cover.pdf[0] cover.png