Add a class open-drawer to any HTML element (Link, button, div, span etc.).

<button class="open-drawer">Open Drawer</button>

Any link having href="/cart" will open the cart drawer

<a href="/cart">Cart</a>

Open cart drawer programmatically

// It opens the cart drawer with existing cart data
unicart.helpers.ajaxCart.show(); 

// If you need to open cart drawer fresh cart data
unicart.helpers.ajaxCart.load();