Question related to my and wife's US resident alien status, required for USA ITR filling

Whether your wife has a Social Security Number is irrelevant to whether she is a resident alien. Anyone who passes either the Green Card Test or the Substantial Presence Test is a resident alien. You are a resident alien for all of 2020 because you pass the Substantial Presence Test for 2020. Assuming that your wife has not been in the US in previous years, she does not pass the Substantial Presence Test for 2020, and is therefore by default a nonresident alien for all of 2020. Nonresident aliens cannot file jointly (unless treated as resident), so by default you would have to file as Married Filing Separately.

However, since you are a resident alien, you guys can choose to use the Nonresident Spouse Treated as Resident option, which treats your wife as a resident alien for all of 2020, and requires you guys to file as Married Filing Jointly. Note that being a resident alien means that your wife's worldwide income for the whole year would be subject to US tax, and would need to be reported on your joint tax return, though she may be able to use the Foreign Earned Income Exclusion to exclude US tax on foreign income from the part of the year before she came, and/or use the Foreign Tax Credit to avoid double taxation.