There's no magic here. I too am an engineer, and find sales work yucky. If you want to make more than 5$ an hour on upwork and you're not about working a "real job" sales work is going to be an unfortunate fact of life.
Given that a contract is probably worth 50k+ to your wife, traditional sales approaches are probably a good fit. Unless she wants to do data-set building, I would assume that her target businesses are sophisticated enough to be keeping data. So start there, make a list of businesses that fit the profile, find contacts (put them in a spreadsheet) and start calling or emailing. No magic, just a grind and a lot of rejection.
In terms of a longer-term strategy, she might pursue some sort of content strategy and start funnelling traffic to her website that way. Some % of that will convert to leads and some % of those will convert to clients. Once you get that pipeline set up, you can spend infinite time optimizing whatever parts of that pipeline. I assume though, that in the short-term, she needs work now and not x months from now. "Traditional sales" are likely a better fit in that case.
She might also consider joining a referral network like BNI if there's a local chapter(s) that look like there are enough members that fit your target profile.
And as the other commenter mentioned, your first port of call should be friends and family. Don't harangue them for a sale, just let them know your shingle is out. Presumably some % of them want you to succeed and you'll probably get a lead or two kicked your way in fairly short order.
But hasn’t someone solved this inefficiency? Hasn’t someone created a marketplace for buyers and sellers of PhD-level data analysis to find each other?
You don't want to participate in such a market even if it exists. Your wife is a human being and a professional, not a faucet. Participating in an undifferentiated labor market commodifies her and turns her into the latter rather than the former.
In those types of market places, the primary way for participants to differentiate themselves is price. It's not like you can exercise a lot of control over how any given platform is going to let you market. A bunch of people competing on price without being able to effectively differentiate in any other way is going to have predictable and unpleasant results.
So yeah, doing sales work sucks. But it doesn't suck as bad as the alternatives.
If you/your wife go down the road of trying to source hourly contracts from such markets, you're setting her up for a working situation that's almost strictly shittier than working a "real job." It's basically impossible to rack up 40 billable hours a week on a consistent basis. 25-30 is much more realistic. If she's charging 50/hr, that'll work out to about $58,000 gross a year assuming 75% utilization and that none of her clients ever flake out. Nevermind that the work is more precarious than a "real job", doesn't have insurance or other benefits, and you get slammed with self employment taxes. Also, you/she don't even get to count on a paycheck at any particular interval. If you provide net 30 (I don't recommend, but it's fairly standard,) you have to have enough of a financial buffer to deal with clients cutting you all of your invoices at once instead of as you bill them. Enjoy praying for the mailman to come before the bank closes so you can pay rent.
Finally, I assume your wife didn't spend 6-10 years of her life grinding out a PhD so she can make 58k a year in the most precarious possible way. Get off of this freelancer mentality, start a business, deliver real value, and get her the income and respect she deserves. If you/she bill yourself out like a commodity, people and businesses are going to treat you like one.
In your case, I would suggest that your wife reach out to her dissertation advisers, or anyone who can vouch for her work, and ask them if they know of anyone that would benefit from her skill set.
Networking is going to be key for customer acquisition. Keep a lookout for data science related conferences in your area, as that will attract attendees in the same field, who may have leads available as well.
By networking. Even smaller towns nowadays have specific community events that are worth attending just for the networking part. If you can't find one about data science or AI, try going to the local Web development meetup and, for example, connect with people who need or are passionate about data visualizations.
You can also reach out to businesses directly by cold contacting, if you can't get a warm introduction. You'll get used to hearing no a lot, but that's a valuable experience in and of itself.
Caveat that networking is a slow "long term growth" activity. If she needs work now, researching businesses that fit a target profile and cold calling is the name of the game.
Given that a contract is probably worth 50k+ to your wife, traditional sales approaches are probably a good fit. Unless she wants to do data-set building, I would assume that her target businesses are sophisticated enough to be keeping data. So start there, make a list of businesses that fit the profile, find contacts (put them in a spreadsheet) and start calling or emailing. No magic, just a grind and a lot of rejection.
In terms of a longer-term strategy, she might pursue some sort of content strategy and start funnelling traffic to her website that way. Some % of that will convert to leads and some % of those will convert to clients. Once you get that pipeline set up, you can spend infinite time optimizing whatever parts of that pipeline. I assume though, that in the short-term, she needs work now and not x months from now. "Traditional sales" are likely a better fit in that case.
She might also consider joining a referral network like BNI if there's a local chapter(s) that look like there are enough members that fit your target profile.
And as the other commenter mentioned, your first port of call should be friends and family. Don't harangue them for a sale, just let them know your shingle is out. Presumably some % of them want you to succeed and you'll probably get a lead or two kicked your way in fairly short order.