Investing in the US market being a foreigner

[Franz Isak Bergmann Ingolfsson]

I have been following BiggerPockets for a year now as well as my real estate in my whole country, Iceland which contains only 360.000 people and I can't see any deals that give a good cashflow, the best thing you can do when investing here is flipping and holding apartments and hoping they will appreciate. That got me thinking if it's allowed for a foreigner with hard cash like me to invest in the US market without actually living there or having any kind of permit like the green card?