Start with your network (assuming you have at least a few senior engineers and your career is 4+ years in tech, you should have this via LinkedIn). You are looking for folks you worked with that are now at their 2nd+ job in their career with mostly smaller companies (generally start-ups, 5-100 full-time, 1-50 eng teams) or are now involved with venture capital/investing/anything that suggests they have exposure to smaller teams. These are the companies with high chance of having a contract role open either because they are growing too fast or they just have lots of stuff to build but don't necessarily want to/can spend time on hiring.
From there reach out and ask them for help and provide your skillset, goals (X length contract work with mobile focus), and see if they will help connect you further. Hopefully your resume and past experience with that connection help you get your foot in the door more easily.
Put your resume on Indeed and Dice, and keep a google voice number, you will get a lot of calls from "offshore recruiters" working for primary and secondary vendors.
Yes, they are real jobs. But you have to make sure that it is from primary vendors. Often times, many secondary vendors source for the same job listed by primary vendor. One way to cut down secondary vendors, ask for decent rates. If someone asks you to work for $60 per hr, just say NO.
Even primary vendors have outsourced their recruiting to India.
$60/hr as a contractor is the equivalent of $30/hr or less salaried. At $60/hr, it's probably even less than $30/hr because you are not eligible for ACA tax breaks and must pay full price for health insurance. The health insurance plans available on the individual market have large premiums and deductibles compared to plans that employers subsidize. You also have a larger tax burden, including the need to file quarterly.
The rule of thumb for contracting is to take your salaried rate and double it at minimum.
If you can bill 40 hours/week for 50 weeks per year, that's about 2K hours so $120K/year. But you can't. You'll probably do well to bill half that because contracts probably don't fill basically the entire year neatly like that. You probably also want to budget time anyway for vacations/illness/etc., selling, billing, learning, and all the other off-the-clock things you need to do.
So now you're closer to $60K per year and that's with self-employment tax and no benefits including health (unless you're on a partner's plan).
So at $60/hr, even with a fairly full calendar, you're pretty much scraping by in the US.
For contract position in the U. S.? Where total comp is going to be...$60/hour, and you pay your own health insurance? For an IC role better than junior, I'd laugh as I hung up the phone...ten years ago. And I'm nothing special, just a grunt with a decent resume.
Backend. Can't think of any speciality skills unfortunately. Generally building, testing, shipping and maintaining services. Familiar with C#/.NET and Python/Django.
From there reach out and ask them for help and provide your skillset, goals (X length contract work with mobile focus), and see if they will help connect you further. Hopefully your resume and past experience with that connection help you get your foot in the door more easily.