I've seen it out here often.  It's an issue with multiple boards, data shares and the feeds to the IDXs happening faster and more reliably than the shares between MLSs.

Technically (not considering any ethics/policies), there are two ways this could happen: 1. The seller/agent claims it on Zillow and posts it for sale on their own or 2. the brokerage is feeding listings to Zillow via their website (not straight from the MLS) and the listing is inputed on the website first.

Could the listing agent or seller have entered it early?

It doesn't.

It takes Z 24-48 hours to show our listings...if we allow them show.

Many we do not, now that they are a brokerage especially...it just depends on how brainwashed our clients are by the Z factor.

An agent with too much time in their hands entering it manually into Z in an effort to circumvent the clear cooperation rules?

mostly like via a different MLS or a brokerage site that feds zillow

It must be possible if you are seeing it ... right? 

The strategy is to post a listing on my website first, get it indexed by G, then post on MLS and other sites. 

Agents are compelled to dance with the devil by their associations, brokerage and franchise.
Leaves me feeling dirty knowing everything ends up on Zdevils website regardless of what I try to do within the lines.
Opportunity exists for the enterprise with vision.

What Melanie said is possible. Seller added it in or agent added it in before the MLS feed kicked in. I don't see a benefit though.

I've personally added them when they mysteriously don't show up.

I have never noticed. I do know our mls feeds to Zillow and many other real estate websites.

You may find the last paragraph from this RISMedia post from September of last year, of some significance/explanation to your question...
From Portal to Brokerage: Zillow Takes Massive Next Step Into All-in-One Real Estate Services

Z answer is a mystery to me Peter...spend little time there.