Any suggestions where we should look for work and how should we go about getting our first clients? I understand that there are freelancing sites but not sure if they have good work or if they are a good place to start.
Also, what you are describing is like opening a mechanical engineering shop and saying "we can invent anything that moves". Consider how well that would go. Specialization is the key, at least in the early stages.
If you are good at some domain and believe you can help someone in that domain, you can create and demonstrate your analyses with specific examples. In addition, building a decent blog with personal touch and experience can create "collateral" and it helps keep you make continuous progress in small steps without necessarily focusing on any specific topic.
Follow up periodically so that the company stays in your deal flow pipeline and maybe it leads to work at some future date. Maybe it doesn't.
Doesn't matter what magic the consultancy sells, that's how it works: build a big enough pipeline of potential sources of work and statistically there is always likely to be enough work to keep the lights on. Statistically, if the pipeline is not big enough, there won't be.
The size of the pipeline is based on the rate at which the consultancy burns through money; the aggregated probabilities of each potential client to produce paying work each month; the rates at which clients cancel projects, fail to pay, or choose an alternate means of accomplishing their goal; and the amount of time it takes to complete a project (e.g. $10k over two years versus $10k over two weeks).
The larger the consultancy, the bigger the pipeline needs to be. My advice is to start putting numbers into Excel.
Good luck.
When I go back down this path, I'm hoping to bootstrap with a Blog instead. Not necessarily because I think this is the best idea, but because I think it will be more fun.
For most consulting jobs, the client has a clearer idea of what they are going to get. You might promise them a working SAP system, advice on a document they might sign, a tax return they can file and so on.
With data science, you might just be promising them: hey, we will take a look around in the data and see if we can find something interesting.
This is a harder sell. I think you need a clear example of what you might find and why that is valuable to the client.
Strategy consulting firms often deal with similar issues. I do think that it is not easy to land pure strategy assignments unless you are already at McKinsey, BCG or Bain.
Talk a look at your local/nearest industries. Pick a medium sized one. Get to know them and take a look at the machines they use for QA.
You'll be very surprised to see that, in some industries, quality test could take dozens of hours (you cannot speed up chemical reactions).
If you can infer the quality of a product based on easy-to-accquire inputs, then you have a customer.
There are tons of free data sets out there, find something in a vertical that you think has a large market share and blog about it. Run and crunch those numbers on your own dime, make your visualizations beautiful.
Hiring a content marketing consultant would be in your best interest and might be cheep.