Since you don't want to specify which of the given coordinates is the origin
(a required parameter in sending Directions Request), an option that you can use is to connect each LatLng locations such as described in Polylines.
A Polyline object consists of an array of LatLng locations, and creates a series of line segments that connect those locations in an ordered sequence.
Here is a sample code to add a Polyline as shown in the documentation:
// This example creates a 2-pixel-wide red polyline showing the path of William
// Kingsford Smith's first trans-Pacific flight between Oakland, CA, and
// Brisbane, Australia.
function initMap() {
var map = new google.maps.Map(document.getElementById('map'), {
zoom: 3,
center: {lat: 0, lng: -180},
mapTypeId: 'terrain'
});
var flightPlanCoordinates = [
{lat: 37.772, lng: -122.214},
{lat: 21.291, lng: -157.821},
{lat: -18.142, lng: 178.431},
{lat: -27.467, lng: 153.027}
];
var flightPath = new google.maps.Polyline({
path: flightPlanCoordinates,
geodesic: true,
strokeColor: '#FF0000',
strokeOpacity: 1.0,
strokeWeight: 2
});
flightPath.setMap(map);
}
After being able to connect all given coordinates, you may also have the option to configure the shapes using polyline's editable and draggable properties with Polyline class.
To help you further with the implementation, you may also refer to suggested solution in this related SO post wherein working code snippets were also provided. Hope it helps!