In case your activities, fragments and UI require some background processing a good thing to use is a MockWebServer which runs localy on an android device which brings a closed and testable enviroment for your UI.

https://github.com/square/okhttp/tree/master/mockwebserver

First step is including the gradle dependency:

testCompile 'com.squareup.okhttp3:mockwebserver:(insert latest version)'

Now steps for running and using the mock server are:

• create mock server object
• start it at specific address and port (usually localhost:portnumber)
• enqueue responses for specific requests
• start the test

This is nicely explained in the github page of the mockwebserver but in our case we want something nicer and reusable for all tests, and JUnit rules will come nicely into play here:

/**
 *JUnit  rule that starts and stops a mock web server for test runner
*/
 public class MockServerRule extends UiThreadTestRule {

 private MockWebServer mServer;

 public static final int MOCK_WEBSERVER_PORT = 8000;

    @Override
    public Statement apply(final Statement base, Description description) {
        return new Statement() {
            @Override
            public void evaluate() throws Throwable {
                startServer();
                try {
                    base.evaluate();
                } finally {
                    stopServer();
                }
            }
        };
    }

    /**
     * Returns the started web server instance
     *
     * @return mock server
     */
    public MockWebServer server() {
        return mServer;
    }

    public void startServer() throws IOException, NoSuchAlgorithmException {
        mServer = new MockWebServer();
        try {
            mServer(MOCK_WEBSERVER_PORT);
        } catch (IOException e) {
            throw new IllegalStateException(e,"mock server start issue");
        }
    }

    public void stopServer() {
        try {
            mServer.shutdown();
        } catch (IOException e) {
            Timber.e(e, "mock server shutdown error”);
        }
    }
}

Now lets assume that we have the exact same activity like in previous example, just in this case when we push the button app will fetch something from the network for example: https://someapi.com/name

This would return some text string which would be concatenated in the snackbar text e.g. NAME + text you typed in.

/**
* Testing of the snackbar activity with networking.
**/
@RunWith(AndroidJUnit4.class)
@LargeTest
public class SnackbarActivityTest{
    //espresso rule which tells which activity to start
    @Rule
    public final ActivityTestRule<SnackbarActivity> mActivityRule = 
        new ActivityTestRule<>(SnackbarActivity.class, true, false);

    //start mock web server
    @Rule
    public final MockServerRule mMockServerRule = new MockServerRule();

    @Override
    public void tearDown() throws Exception {
       //same as previous example
    }
    
    @Override
    public void setUp() throws Exception {
       //same as previous example

       **//IMPORTANT:** point your application to your mockwebserver endpoint e.g.
       MyAppConfig.setEndpointURL("<http://localhost:8000>");
    }
    
    /**
    *Test methods should always start with "testXYZ" and it is a good idea to 
    *name them after the intent what you want to test
    **/
    @Test
    public void testSnackbarIsShown() {
        //setup mockweb server
        mMockServerRule.server().setDispatcher(getDispatcher());

        mActivityRule.launchActivity(null);
        //check is our text entry displayed and enter some text to it
        String textToType="new snackbar text";
        onView(withId(R.id.textEntry)).check(matches(isDisplayed()));
        //we check is our snackbar showing text from mock webserver plus the one we typed
        onView(withId(R.id.textEntry)).perform(typeText("JazzJackTheRabbit" + textToType));
        //click the button to show the snackbar
        onView(withId(R.id.shownSnackbarBtn)).perform(click());
        //assert that a view with snackbar_id with text which we typed and is displayed
        onView(allOf(withId(android.support.design.R.id.snackbar_text), 
        withText(textToType))) .check(matches(isDisplayed()));
    }
    
     /**
     *creates a mock web server dispatcher with prerecorded requests and responses
     **/
    private Dispatcher getDispatcher() {
        final Dispatcher dispatcher = new Dispatcher() {
            @Override
            public MockResponse dispatch(RecordedRequest request) throws InterruptedException {
                if (request.getPath().equals("/name")){
                    return new MockResponse().setResponseCode(200)
                            .setBody("JazzJackTheRabbit");
                }
                throw new IllegalStateException("no mock set up for " + request.getPath());
            }
        };
        return dispatcher;
    }

I would suggest wrapping the dispatcher in some sort of a Builder so you can easily chain and add new responses for your screens. e.g.

return newDispatcherBuilder()
           .withSerializedJSONBody("/authenticate", Mocks.getAuthenticationResponse())
           .withSerializedJSONBody("/getUserInfo", Mocks.getUserInfo())
           .withSerializedJSONBody("/checkNotBot", Mocks.checkNotBot());