Hi Abhinav,
Congratulations! You would be able to apply for PR once you guys are in Canada. Since the baby is born is US he/she will have the US passport. You can secure the tourist visa and apply for extension based on how the PR process has progressed for the baby.
I also did read that its better to have 1 year of taxes filed before you apply for PR to solidify the case.
We are considering these options since we are also almost in the similar condition as you. The only problem presently is the Covid crisis and how long obtaining a passport/visa would be!
Good luck:)
Reference threads: Bringing non-PR child into Canada
Thanks!
A