JSFiddle - React, Tailwind, and code Playground

HTML

<div class="form-group">
    <label class="col-md-4 control-label" for="IniciarTarefa" id="acao"></label>
    <div class="col-md-4">
        <button id="IniciarTarefa" name="IniciarTarefa" class="btn btn-info">Iniciar Tarefa</button>
    </div>
</div>
<button id="mostrar">Mostrar quando tarefa foi iniciada</button>

JavaScript

$('#IniciarTarefa').on('click', function () {
    $(this).closest('.form-group').data('inicio', new Date().getTime());
});

$('#mostrar').on('click', function () {
    var time = $('.form-group').data('inicio');
    alert(new Date(time));
});