Will a 1-year Data Science Master’s from a private university affect my chances of getting into a PhD at a public university?

I’m currently going to pursue a 1-year Master’s in Data Science from a private university because I wasn't qualified enough. I’m genuinely interested in research and considering applying for a PhD at a public university after gaining some experience in the field.

Will the fact that my Master’s is only one year and from a private institution limit my chances or eligibility for PhD programs at public universities (especially in the U.S. or Europe)?

Any advice or experiences would be really helpful!