I think a little JS would do it. The following gets the start and end of the month:
var firstDay = new Date(new Date().getFullYear(), new Date().getMonth(), 1);
var lastDay = new Date(new Date().getFullYear(), new Date().getMonth() + 1, 0);
let foo = [firstDay, lastDay]
return foo
So in your SQL, you could write:
SELECT
some_stuff
FROM
some_tables
WHERE
some_criteria = 'Awesome'
AND schedStartTime >= {{ new Date(new Date().getFullYear(), new Date().getMonth(), 1) }}
AND schedStartTime < {{ new Date(new Date().getFullYear(), new Date().getMonth() + 1, 0) }}