Angular/Primeng - Implement p-autocomplete dropdown with no button - html

Question

I have a "p-autocomplete" element with multiple entries and dropdown enabled, and am wondering if I can do so without displaying the button, but instead show the dropdown menu when users click on the autocomplete field.
Is this possible with this type of object?
I am using Primeng version 4.3.0, if it makes a difference.
HTML:
<p-autoComplete id="input-country" [multiple]="true" [(ngModel)]="selectedCountries" [dropdown]="true"
[suggestions]="filteredCountries" (completeMethod)="filterCountryMultipe($event)">
<ng-template let-selectedCountries pTemplate="item">
....
</ng-template>
</p-autoComplete>
===================
UPDATE=====================
Thank you to olivier-depriester for your answer below. In addition to the onFocus method, I also removed the dropdown property and handled everything with the autocomplete, simply amending the filter method to accept an empty query.
Current HTML:
<p-autoComplete id="input-country" [multiple]="true" [(ngModel)]="selectedCountries" (onFocus)="onFocus()"
[suggestions]="filteredCountries" (completeMethod)="filterCountryMultiple($event)" >
<ng-template let-selectedCountries pTemplate="item">
....
</ng-template>
</p-autoComplete>
Current Typescript:
onFocus(){
this.filterCountryMultiple({query:''});
this.autoComplete.show();
}
filterCountryMultiple(event) {
let query = event.query;
this.filteredCountriesMultiple = this.filterCountry(query);
}
filterCountry(query):any[] {
....
for(let i = 0; i < countries.length; i++) {
let country = countries[i];
if(...query is empty...){
filtered.push(country.code);
}
else if(...match found...) {
filtered.push(country.code);
}
}
return filtered;
}

Answer 1

With primeng 6.5 to 7.0, I used the show function, bound on the focus event.
On typescript side :
export class MyComponent {
#ViewChild(AutoComplete) private autoComplete: AutoComplete;
onFocus() {
this.autoComplete.show();
}
}
And on HTML side :
<p-autoComplete id="input-country" [multiple]="true" [(ngModel)]="selectedCountries" [dropdown]="true"
[suggestions]="filteredCountries"
(completeMethod)="filterCountry($event)"
(onFocus)="onFocus($event)">
<ng-template let-selectedCountries pTemplate="item">
<div class="ui-helper-clearfix" style="border-bottom:1px solid #D5D5D5">
.......
</ng-template>
</p-autoComplete>
But in primeng current version (v8), this method is no more documented. So I don't know if it still exists