You can get what you need with a a regex of the form
"\^\QJ\E"
. The whole query will look like the following:curl -H "X-Parse-Application-Id: $app_id" \
-H "X-Parse-REST-API-Key: $api_key" \
-G --data-urlencode 'where={"first_name" : { "$regex" : "^\QJ\E" } }' \
https://api.parse.com/1/users/
Are "like" or regex queries possible via the REST API? | Parse
https://www.parse.com/questions/are-like-or-regex-queries-possible-via-the-rest-api