How to add Different Padding Between Floating Hint and Input Text in Custom TextInputLayout?

What you are asking to do does not seem to be part of the API. You can, however, get the effect you want by adding a clear start drawable to the TextInputEditText.

square.xml

<shape 
    android:shape="rectangle">
    <solid android:color="@android:color/transparent" />
    <size
        android:width="12dp"
        android:height="0dp" />
</shape>

<androidx.appcompat.widget.LinearLayoutCompat
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical"
    android:padding="16dp">

    <com.google.android.material.textfield.TextInputLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:hint="This is a hint"
        android:paddingTop="16dp">

        <com.google.android.material.textfield.TextInputEditText
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:drawableStart="@drawable/square"
            android:paddingStart="0dp"
            android:textColor="@color/black" />

    </com.google.android.material.textfield.TextInputLayout>

    <EditText
        android:layout_width="50dp"
        android:layout_height="wrap_content"
        android:layout_marginTop="8dp" />
</androidx.appcompat.widget.LinearLayoutCompat>

The start drawable will push entered text 12dp to the right while the hint will ignore it.

You may also use the start icon for the TextInputLayout:

app:startIconDrawable="@drawable/square"
app:startIconMinSize="12dp"

Although, you may already have a start icon.