It depends on the kind of work you want to take on. If you want garden variety structural engineering for buildings then the game is played as you see it: hustle, hustle, hustle, and combine that hustle with low fees. Or get lucky but that tends to be an unreliable thing to rely on.
If you have a bit more tolerance for the unique / uncommon projects then the playbook is markedly different. Contractors are always in need of structural design and very often have no one reliable to turn to; there are lots of people practicing structural engineering - that have licenses to do so - but not a lot of structural engineers (at least in the proper sense). While developers, landlords and architects may not know the difference (sorry to say) contractors generally do. As builders we are keen on practicality and cost reduction and we know when a design is just trash or when it's good value engineering.
To put the demand into perspective: I'm a contractor who mostly acts as a GC (other times as a sub-trade) and the amount of engineering work from people I compete with could rival a small design office. And I can assure you, they wouldn't be coming to a competitor for engineering if they had a viable alternative.
What's my point? My point is target the medium sized contractors. Ones who do not have engineers on staff. We are price sensitive but not about your design fees; as long as your design is cheap or efficient to build. Contracting clients will come almost exclusively by word of mouth. You need to pound the pavement for the first couple. But after that, word of mouth will spread a hell of a lot quicker then in the architect / developer world. We share recommendations for good trades and design professionals all the time with our friends and do so gladly.
To get in the door I would suggest creating a list of contractors you want to hit and call to speak with a project manager (not estimating...project managers are who you want to talk to. People with a problem in hand that needs solving. Not people estimating a problem to be solved). Follow that up by sending some literature. Cool designs you've done. Contractors, believe it or not, like cool engineering! Send me a picture of something super funky and neat to show what you can do. Once Covid ends hit up their office in person. Follow-up with something every so often just to keep your name top of mind for when a neat engineering project does come up. They'll call you. And if you perform they'll spread the word in the office. Eventually to the outside.
Oh and the benefit of working for my ilk is that a) we pay better, b) we pay faster, c) our work is almost never boring.
Good luck!
EDIT - thought i'd add an example of something to send the contractors you target. The more temporary work-like it is the better. Contractors generally need stuff designed but it is to facilitate the work rather then anything permanent. So the examples you show should be tailored toward that. Take a look at this example. If you show up at an office with something like this and say "stuff like this is absolutely no problem" I bet they wont even ask about fees before the contractor talks about a project they need some help with (and when can you start).
