I became a permanent resident in January, 2020. But I do not have a Social Security card. Can I still get the stimulus check?
One thing that isn't super well known is that the stimulus check is actually a credit toward your 2020 taxes. That is, on paper, everyone is supposed to get a credit for their 2020 tax bill, that wouldn't be completely calculated until you do your forms in early 2021. However, the need to stimulate the economy is for today, so what the federal government is doing is using whatever information they have on you to estimate what your credit for 2020 would be and then paying that out as soon as possible.
What this means is that if you have filed your 2019 return, the government assumed that what you made in 2019 will be what you make in 2020, and pay your tax credit based on that. If you have not filed your 2019 return yet (deadline has been extended so it is not late, yet), they will use your 2018 return. And if you haven't had to file any return the last two years for whatever reason -- you can contact the IRS and give them your info:
"Who is eligible for the Economic Impact Payment? U.S. citizens, permanent residents or qualifying resident aliens who:
Have a valid Social Security number, Could not be claimed as a dependent of another taxpayer, and Had adjusted gross income under certain limits."
If you dont have a social security number yet, then it looks like you are not eligible. However, again, this is formally a credit to your 2020 taxes. If you dont get a check in the near future, there will be a worksheet to calculate your credit that would be applied to your 2020 return.