after removing activity as default launcher how to start activity in android

That is impossible.
Because as you removed the category of activity as Launcher, the Android system won't be able to understand which activity need to be started when application is requested to be opened.
Therefore you must specify Launcher activity in Manifest.xml file, like this,

<activity android:name=".ExampleActivity" android:icon="@drawable/app_icon">
    <intent-filter>
        <action android:name="android.intent.action.MAIN" />
        <category android:name="android.intent.category.LAUNCHER" />
    </intent-filter>
</activity>

To overcome this, you need to use Explicit Intents,
Activities that you don't want to make available to other applications should have no intent filters and you can start them yourself using explicit intents.

Read this Intent[^]

Quote:

Explicit intents specify the component to start by name (the fully-qualified class name). You'll typically use an explicit intent to start a component in your own app, because you know the class name of the activity or service you want to start. For example, start a new activity in response to a user action or start a service to download a file in the background.

for example,

Intent intent = new Intent(this, SignInActivity.class);
startActivity(intent);

-KR