Is possible to using js to make a group selected and click it?

@dfsd_3534 – Try this code (the task would be much simpler and faster without multiple artboards):

#target photoshop

// Get the active document
var doc = app.activeDocument;

// Find all the 'design' layer groups in the document
var designGroups = getDesignGroup(doc.layers);

// If there's at least one 'design' group, select the first one
if (designGroups.length > 0) {
    doc.activeLayer = designGroups[0];
} else {
    alert("No 'design' layer group found.");
}

// Function to loop through all layer groups and find the child group named 'design'
function getDesignGroup(layerSet) {
    var groups = new Array();

    for (var i = 0; i < layerSet.length; i++) {
        var layer = layerSet[i];

        // If the layer is a layer group
        if (layer.typename === 'LayerSet') {
            // If the layer group case-sensitive name is 'design'
            if (layer.name === 'design') {
                groups.push(layer);
            } else {
                // Recursively search in subgroups
                var subGroups = getDesignGroup(layer.layers);
                groups = groups.concat(subGroups);
            }
        }
    }
    return groups;
}

app.activeDocument.activeLayer = targetGroup;

By @dfsd_3534

Where/how is the variable for targetGroup defined?

Is there only one group in the doc?

Does the group have a unique specific name to select by?

Does the group have a specific position in the layer stack?

Are artboards ever in use?

The screenshot seems to indicate that the group is selected. 

Sorry for my typo in title