JSFiddle - React, Tailwind, and code Playground
HTML
<input id="date" type="date" value="2017-06-01">
CSS
input[type=date] {
border: 0;
clip-path: inset(0 17px 0 0);
width: 120px
}
<input id="date" type="date" value="2017-06-01">
input[type=date] {
border: 0;
clip-path: inset(0 17px 0 0);
width: 120px
}