In your component, try this:

ngOnInit() {
    this.filteredOptions = this.myControl.valueChanges.pipe(
      startWith(this.myControl.value), <--- this
      map((value) => this._filter(value || ''))
    );
  }

and in the html
<mat-autocomplete [autoSelectActiveOption]="true" #auto="matAutocomplete" [autoActiveFirstOption]="true">

I guess that the icon just appears when you select by yourself an option. I checked the mat-autocomplete api and there's no way to do it. Also tried to add the [selected] in the mat-option without any good results.

#27652 Here was a bug fixing with resetting. In my opinion, it is a fair and very useful feature to set the initial value without all these steps described by @GCancinoH above.

In addition to this issue, I noticed if you attempt to capture the first and last options using the MatAutocomplete class, it retains the original values when the list was originally set and filtered. This used to work in Angular Material version 13/14 but no longer does. I do believe both of these issues have something to do with how options are set as selected.
choose-first-option.txt

Any plans to fix this issue?