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Can a F1 student start their own company and sponsoring themselves?

See my response above. After they graduate, it's much easier, OPT and under certain circumstances STEM OPT permit this.

Thank you for your response! Which type of greencard should be used by the startup LLC?

What options are available for a F1 visa holder to get greencard through his/her own startup?

The same as everything else. Green cards and visas are largely independent and one does not depend on the other.