US topco: LLPs take about a month to create (formation, getting a bank account, starting the ODI process). Then the paperwork for the US parent takes just minutes to handle. Subsequently setting up a wholly owned subsidiary in India (a private limited company) takes about another month or so.
India topco: setting up a India Private Limited (Pvt Ltd) company takes a few weeks to do fully. The US subsidiary just takes a few minutes. Wiring the ODI payment from the Indian parent to US subsidiary takes a week or two more.
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