How long is the non-compete clause for? Just an fyi, those things are usually pretty much nothing more than a legal scare tactic. Not telling you to just disregard it or anything, but noncompetes and NDA's are nothing more than legal scare tactics. It's just there for a bigger company to try and bleed someone else dry through court costs.
But to your answer, short term you should really just cold call and do some walk ins. It's not fun at all, but there's really no other way so soon. A bit longer term, I'd look into establishing a bit of a web presence. The courier companies around me have weak websites, and it would be easy to overcome their spots in the google search. Reviews are very important for this. Try to get any customer of your to leave you a review.