Hello! Co-working spaces are places that people enjoy going to, especially mini startups, sole proprietors, developers, designers, etc. So at least you know there can be a market.
Now, to figure out exactly which is your target market, you can do so by literally "asking" people... (not like you're used to).
What I would do in your position is to run Facebook Ads in the area immediately surrounding the space (this can be done quite easily). The interesting part comes when choosing the audience:
Instead of "throwing" your ads to everyone, you can specify individual interests (like certain tools, software programs, niche magazines, etc) and behaviors (small business owners, Facebook page admins, etc).
Once you've segmented your audience, you can create a tailored ad that "speaks" specifically to their person. That way they will fell identified and most likely click on it.
You would then send them to a landing page that talks about your space and what it will solve for them.
If the space itself is still not ready, you can take advantage of this and simply use the landing page to capture interested people's names and emails. That way, you'll gain two things:
1. A prospect (lead) list that you can contact once it is ready
2. Knowledge of which market segment most responded to your ads and landing pages
You will then use all this to continuously grow your business. :)
Need help figuring out how to do this exactly? Let me know and we can either teach you or your staff or do it for you.