Update[24/04/19]:
I just found out that the library already provide us a way to listen to empty initial load, using PagedList.BoundaryCallback<YourItem>. 
*Note that my old answer is still a valid alternative.
val livedPageList = LivePagedListBuilder(sourceFactory, config)
        .setBoundaryCallback(object: PagedList.BoundaryCallback<YourItem>() {
            override fun onZeroItemsLoaded() {
                super.onZeroItemsLoaded()
                // Handle empty initial load here
            }
            override fun onItemAtEndLoaded(itemAtEnd: YourItem) {
                super.onItemAtEndLoaded(itemAtEnd)
                // Here you can listen to last item on list
            }
            override fun onItemAtFrontLoaded(itemAtFront: YourItem) {
                super.onItemAtFrontLoaded(itemAtFront)
                // Here you can listen to first item on list
            }
        })
        .build()
Original Answer:
Based on this class on google sample Network State. Modify it to handle empty content in initialLoad.
@Suppress("DataClassPrivateConstructor")
data class NetworkState private constructor(
    val status: Status,
    val msg: String? = null
) {
    enum class Status {
        RUNNING,
        SUCCESS_LOADED, // New
        SUCCESS_EMPTY, // New
        FAILED
    }
    companion object {
        val EMPTY = NetworkState(Status.SUCCESS_EMPTY) // New
        val LOADED = NetworkState(Status.SUCCESS_LOADED) // New
        val LOADING = NetworkState(Status.RUNNING)
        fun error(msg: String?) = NetworkState(Status.FAILED, msg)
    }
}
Usage as follow:
class DataSource: PageKeyedDataSource<Long, Item>() {
    val initialLoad: MutableLiveData<NetworkState> = MutableLiveData()
    override fun loadInitial(params: LoadInitialParams<Long>, callback: LoadInitialCallback<Long, Item>) {
        initialLoad.postValue(NetworkState.LOADING)
        apiCallSource.subscribe({ items ->
            if (items.isEmpty()) {
                initialLoad.postValue(NetworkState.EMPTY)
            } else {
                initialLoad.postValue(NetworkState.LOADED)
            }
        }, { error -> 
            // handle error
        })
    }
}
And this is how the activity handle it:
class activity: AppCompatActivity() {
    val viewModel = // init viewmodel
    override fun onCreate(savedInstanceState: Bundle?) {
        viewModel.refreshState.observe(this, Observer { networkState ->
            if (it == NetworkState.LOADING) {
                // Show loading
            } else {
                // Hide loading
                if (it.status == NetworkState.Status.SUCCESS_EMPTY) {
                    // Show empty state for initial load
                }
            }
        }
    }
}
For more details on how to connect DataSource with Activity, see this sample
Simply add a listener or callback function to your DataSourceFactory and your DataSource and call it if the list in loadInitial is empty:
class DataSourceFactory(
    private val dataObservable: Observable<List<Data>>,
    private val onEmptyAction: () -> Unit
) : DataSource.Factory<Int, Data >() {
     override fun create(): DataSource {
         return DataSource(observable, onEmptyAction)
     }
}
class DataSource(
    private val observable: Observable<List<Data>>,
    private val onEmptyAction: () -> Unit
) : ItemKeyedDataSource<Int, Data>() {
    private val data = mutableListOf<Data>()
    override fun loadInitial(params: LoadInitialParams<Int>, callback: LoadInitialCallback<Data>) {
        observable
            .subscribe({ data ->
                if (data.isEmpty()) {
                    // Inform someone that this list is empty from the
                    // beginning to be able to show an empty page
                    onEmptyAction()
                }
                // rest of your code & logic
        }, { Timber.e(it) })
    }
}
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