You can do this in a commandlet to import assets:
FAssetToolsModule& AssetToolsModule = FModuleManager::LoadModuleChecked("AssetTools");
TArray<UObject*> ImportedObjects = AssetToolsModule.Get().ImportAssets(FileToImport, PackagePath, FactoryToUse);
FactoryToUse is optional. If you don’t specify one it will figure it out. However the major problem with FBX is that a dialog appears asking for FBX settings. FBX’s are complicated and we cant easily determine in all cases what is in the file and what the user wants without asking ( and there could be multiple things in the file). You are going to have to work around this. I suggest constructing your own UFbxFactory instance, passing it in to the method above and adding some method to the UFbxFactory to specify the settings up front and not show the dialog. There is some basic auto-detection of asset type in the FBX file so simply adding a flag to not show the dialog and use the defaults might work out OK for you.