JSFiddle - React, Tailwind, and code Playground
HTML
<select id="the-select">
<option></option>
<option>A</option>
<option>B</option>
</select>
<button id="the-button">
click me!
</button>
JavaScript
document.getElementById("the-button").addEventListener("click",()=>{
let sel = document.getElementById("the-select");
sel.showPicker();
});