Bottom app bar problem with placing icons

You can place a custom layout inside your BottomAppBar. The only thing is that you will need to align items in your custom layout manually.

<com.google.android.material.bottomappbar.BottomAppBar xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    style="@style/Widget.MaterialComponents.BottomAppBar"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:layout_gravity="bottom"
    app:backgroundTint="@android:color/white"
    app:contentInsetLeft="0dp"
    app:contentInsetStart="0dp">

    <androidx.constraintlayout.widget.ConstraintLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content">

        <ImageButton
            android:id="@+id/first_menu_item"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:layout_marginTop="16dp"
            android:layout_marginBottom="8dp"
            android:src="@drawable/ic_first_icon"
            app:layout_constraintBottom_toBottomOf="parent"
            app:layout_constraintEnd_toStartOf="@+id/second_menu_item"
            app:layout_constraintHorizontal_chainStyle="packed"
            app:layout_constraintStart_toStartOf="parent"
            app:layout_constraintTop_toTopOf="parent" />

        <ImageButton
            android:id="@+id/second_menu_item"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:src="@drawable/ic_second_icon"
            app:layout_constraintBottom_toBottomOf="@+id/first_menu_item"
            app:layout_constraintEnd_toStartOf="@+id/placeholder"
            app:layout_constraintHorizontal_chainStyle="packed"
            app:layout_constraintStart_toEndOf="@+id/first_menu_item" />

        <View
            android:id="@+id/placeholder"
            android:layout_width="70dp"
            android:layout_height="0dp"
            android:visibility="invisible"
            app:layout_constraintBottom_toBottomOf="@+id/first_menu_item"
            app:layout_constraintEnd_toStartOf="@+id/third_menu_item"
            app:layout_constraintHorizontal_chainStyle="packed"
            app:layout_constraintStart_toEndOf="@+id/second_menu_item"
            app:layout_constraintTop_toTopOf="@+id/first_menu_item" />

        <ImageButton
            android:id="@+id/third_menu_item"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:src="@drawable/ic_third_icon"
            app:layout_constraintBottom_toBottomOf="@+id/first_menu_item"
            app:layout_constraintEnd_toStartOf="@+id/fourth_menu_item"
            app:layout_constraintHorizontal_chainStyle="packed"
            app:layout_constraintStart_toEndOf="@+id/placeholder" />

        <ImageButton
            android:id="@+id/fourth_menu_item"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:src="@drawable/ic_fourth_icon"
            app:layout_constraintBottom_toBottomOf="@+id/first_menu_item"
            app:layout_constraintEnd_toEndOf="parent"
            app:layout_constraintHorizontal_chainStyle="packed"
            app:layout_constraintStart_toEndOf="@+id/third_menu_item"
            app:layout_constraintTop_toTopOf="@+id/first_menu_item" />

    </androidx.constraintlayout.widget.ConstraintLayout>
</com.google.android.material.bottomappbar.BottomAppBar>

You will have something like this: