An individual's immigration status may be changed while in the United States from nonimmigrant (temporary) to immigrant (permanent). The individual must have been inspected and admitted into the US and the individual must be able to meet all other requirements for a green card. The common term for shifting from temporary to permanent status is "adjustment of status".
FYI: A Green Card is a phrase that refers to an individual's immigration status. The expression refers to an I-551 document (Alien Registration Receipt Card or Permanent Resident Card). The card (which is no longer green) is carried by a lawful permanent resident as proof of their status.