[j0hnik]

FotGOD,
так вы сразу функцию вызываете, вот он и тикает сразу

<div class="container">
		<h2>Home Work 2</h2>
		<div class="box hide"></div>
		<div id="showtime">00:00</div>
		<button id="start" class="btn btn-primary">START</button>
		<br>
		<br>

		<form name="form">
			<div>
				Day: <input id='day_id'>
			</div>
			<div>
				hours: <input id='hour_id'>
			</div>
			<div>
				minutes: <input id='minute_id'>
			</div>
		</form>

	</div>


	<script>

		function  timer(){
			let day= document.getElementById('day_id').value;
			let hour = document.getElementById('hour_id').value;
			let  minute = document.getElementById('minute_id').value;
			let second = 59;
			const now = new Date()
			, newTime = new Date(now.getFullYear()+ 1, 0, 1)
			,  diff = newTime.getTime() - now.getTime()
			, days = day
			, hours = hour
			, minutes = minute
			, seconds = 59 - now.getSeconds()
			;

			let st = '';
			if(diff <= 0) {
				st  = window.open("http://google.com");
			} else {
				st=`${days} days, ${hours} hours,${minutes}minutes,${seconds}seconds`;
			}
			document.getElementById('start').addEventListener('click', timer);

			document.getElementById("showtime").innerHTML = st;
			setTimeout(timer, 1000);
		}
		timer();


	</script>