What is the best and fastest way to get digital marketing clients for a marketer who just started an agency?

I feel you need to laser into a particular market and figure out their biggest challenge and create a landing page that invites them to a webinar that helps them solve their challenge. Drive paid traffic to it and then at the end of the webinar ask them if they need help. That is a good starting point but their is a lot more. You might want to check out http://generateleadseveryday.com

Intensive digital marketing through many channels at the same time to create ur own image.

you should at the beginning to do your homework in your agency, as example you cannot tell any body that you are good in making campaigns on social media and you are not having any references or even you didn't do any campaign for yourself

digital means records for Marketers. always try to provide the numbers in your campaign messages, and your way to handle it, regardless the selected media channels