Using the Advanced properties, you can get the initial View mode (managed by Acrobat) from metadata, check the below code:

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String viewMode = "Fit";
Ref ref = m_doc.Advance_GetRef();
if(ref != null) {
    Obj rootObj = m_doc.Advance_GetObj(ref);
    if(rootObj != null) {
        int count = rootObj.DictGetItemCount();
        for(int cur = 0; cur < count; cur++) {
            String tag = rootObj.DictGetItemTag(cur);
            Obj item = rootObj.DictGetItem(cur);
            if(tag.equals("OpenAction") && item.GetType() == 8) {
                rootObj = m_doc.Advance_GetObj(item.GetReference());
                if(rootObj.DictGetItemCount() > 0 && rootObj.DictGetItem(0).GetType() == 6) {
                    item = rootObj.DictGetItem(0);
                    int arrayCount = item.ArrayGetItemCount();
                    if(arrayCount > 1) {
                        viewMode = item.ArrayGetItem(1).GetName();
                        break;
                    }
                }
            }
        }
    }
}