You can use the data-option: useFocus
Ref: http://dev.jtsage.com/jQM-DateBox2/demos/opt/open.html
Code:
<div id="myPage" data-role="page">
<div data-role="content">
<input name="mydate" id="mydate" type="date" data-role="datebox"
data-options='{"mode":"calbox", "useFocus": true}' />
</div>
</div>