Mission 9 is not the only mission you can get it, Mission 10 when you assault Gudovgrad has the Javelin in it at the final stand against the PLA counter attack
The building you are told to defend has a load of equipment spawn next to it (inc. Queen Bees, Barret .50 and the Javelin) HOWEVER, the US weapons MAY only spawn if you get the LAVs that far, i cannot confirm if this is a requirement
Specifically, the Javelin can be found on the right hand side of the building (when facing the assault) outside the building