I did exactly that in 2017. Landed and activated my PR on a Monday and went for first time H1B stamp following day, Tues morning. No issues
I am in somewhat similar situation now! I am an Indian citizen, currently living in US (India --> Canada --> USA) on exchange visitor visa and my H1B is approved in March 2022. I need H1B stamp.
I lived in Canada in the past and moved to the USA in 2019. I applied for Canadian PR via express entry program in 2018 which was approved in 2019 and PPR was made in late 2019. However, when I sent my passport and documents for visa stamp and COPR in early 2020, due to COVID, passport was returned without any visa stamp or COPR letter and I was asked not to make any travel plans until US-Canada border opens. Later on, my EE online application was updated as - "Counterfoil" valid until 2030; COPR "invalid" with expiry date in 2030!
I don't have valid COPR - I assume the status will change to "valid" at POE?
In summary - I need Canadian PR card, and H1B stamp on my passport. I will prefer H1B stamp in Canada vs in India because Dropbox system in India is not very time sensitive.
My question - Would I be able to visit Canada without any visa stamp in my Indian passport and get H1B stamp on next day or so? Will I be sent back to the USA from the Canadian airport since I don't have any valid Canadian visa stamp?
Please let me know if anyone can help or suggest any resources or provide information regarding how to reach CIC officials to get information.
Thank you