Officially Morocco was the first country to recognize US independence American-Morroco Treaty of Friendship, you might ask why Morocco was the first to recognize the US; it is cause at the time Sultan Mohammed III was trying to make Morocco a stronger power in the region. US trade ships were being attacked by Morocco's neighbors (the Barbary pirates), and thus the Sultan saw a good chance to "show off" his new power and possibly gain a new ally/trade partner, and thus decided to grant "protection" to these US trade ships and recognize the US their independence.

Informally however you could also make a case for the Dutch being the first to recognize the US their independence. The Dutch republic had been supporting the American rebels for a long time, selling them arms and giving them loans, much of this trade took place on the Dutch island colony of "Sint Eustatius", during one of these trades the US ship Andrew Doria was flying the new US flag and while entering port and fired a gun salute, which was answered by the Dutch fort by a gun salute of their own and thus acknowledging the US flag and with that acknowledging the US "existence".

Though the dutch did not sign any treaties with the US before Morocco and thus Morocco was first to officially recognize the US.