Play it a lot. That harsh zing will go away after a while.
You could also deliberately add some sort of grase/gunk, but that isn't too good of a solution.
Best solution is to change all strings once a string breaks, so they can all mellow out evenly again.
If you find you hate the sound of new strings in general, you could think of getting flatwounds. They sound like old roundwounds right from the start, and can be played for years, even decades in some cases. They still sound a bit diffrent from old roundwounds though.
This site has great comparisons of flats vs rounds:
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