Can my wife (H4) apply for H1B on April 1 from India and come to US in May?

Can my wife (on H4) apply for H1B on April 1, while she is in India - and come back to US in May on H4?

What will she need to do to convert from H4 to H1B once she is in US.

Is the COS process smooth? I dont want her to visit any consulate.

Thanks

She can apply for H-1 while she is in India and later travel to US on H-4.

She can later apply for COS from H-4 to H-1 once the petition has been approved. It takes 2-3 months to process and doesn’t run into issues as long as you have all the right documents and have maintained legal status in US.