Opening Google Play in popup (like Vimeo, Wisher, Buzzfeed) - Instant App

I think you're looking for showInstallPrompt.

TL;DR:

InstantApps.showInstallPrompt(activity, 
                              postInstallIntent, 
                              Constants.INSTALL_INSTANT_APP_REQUEST_CODE, 
                              referrerString);

At Vimeo we're using Branch for our web -> mobile app install as well as our instant app -> mobile app install (since it gives some additional metrics and lets us compare the referrers a little better).

If you're interested in using Branch, the documentation for the install prompt can be found here. And the usage looks like:

if (Branch.isInstantApp(this)) {
  myFullAppInstallButton.setVisibility(View.VISIBLE);
  myFullAppInstallButton.setOnClickListener(new OnClickListener() {
    @Override
    public void onClick(View v) {
       BranchUniversalObject branchUniversalObject = new BranchUniversalObject()
           .setCanonicalIdentifier("item/12345")
           .setTitle("My Content Title")
           .setContentDescription("My Content Description")
           .setContentImageUrl("https://example.com/mycontent-12345.png")
           .setContentMetadata(new ContentMetadata()
                 .addCustomMetadata("property1", "blue")
                 .addCustomMetadata("property2", "red"));

      Branch.showInstallPrompt(myActivity, activity_ret_code, branchUniversalObject);
    }
  });
} else {
  myFullAppInstallButton.setVisibility(View.GONE);
}

Branch's implementation ultimately calls through to the API mentioned in the other answer here.

Which looks like:

public static boolean showInstallPrompt(Activity activity, 
                                        Intent postInstallIntent, 
                                        int requestCode, 
                                        String referrer)

Shows a dialog that allows the user to install the current instant app. This method is a no-op if the current running process is an installed app. You must provide a post-install intent, which the system uses to start the application after install is complete.

You can find an example usage here. And looks like the following:

class InstallApiActivity : AppCompatActivity() {


    /**
     * Intent to launch after the app has been installed.
     */
    private val postInstallIntent = Intent(Intent.ACTION_VIEW,
            Uri.parse("https://install-api.instantappsample.com/")).
            addCategory(Intent.CATEGORY_BROWSABLE).
            putExtras(Bundle().apply {
                putString("The key to", "sending data via intent")
            })

    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        setContentView(R.layout.activity_install)

        val isInstantApp = InstantApps.isInstantApp(this)

        findViewById<Button>(R.id.start_installation).apply {
            isEnabled = isInstantApp
            // Show the installation prompt only for an instant app.
            if (isInstantApp) {
                setOnClickListener {
                    InstantApps.showInstallPrompt(this@InstallApiActivity,
                            postInstallIntent,
                            REQUEST_CODE,
                            REFERRER)
                }
            }
        }
    }

    companion object {
        private val REFERRER = "InstallApiActivity"
        private val REQUEST_CODE = 7
    }
}

It's not recommended because it's deprecated, but you can technically get the dialog to show using the following code:

InstantApps.showInstallPrompt(activity, Constants.INSTALL_INSTANT_APP_REQUEST_CODE, null);

See also: https://stackoverflow.com/a/47666873/1759443