Can I get house mortage without social security ID?

I am student in USA enrolled recently to the university and I will stay for about 4 years.
My VISA is F-1 student VISA
currently I am living in rented apartment but I would like to have my own house then I will sell it lonce I finish..
I do have monthly income of about 4000 dollars in addition to my health insurance.
Can I have house mortage without SSN ?
If not, how can I get it since my VISA is F-1 ( student visa)?
How can I get the SSN since my VISA is F-1
I wanted to add that I am living in IA and I already have credite account.

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