Smaller companies generally have less red tape to getting contractors, more need (as they are either scaling quickly OR just need something done and don't want to incur high cost of a perm eng). You will need to figure out the appropriate rate (keeping in mind this doesn't come with benefits), but that exercise is left to the reader.
Hiring is faster, yes, but onboarding is often still a dreadful mess. At least if it's at a company that expects you to use their equipment and their closed system.
I've just been ignoring anything from an Indian sounding name as they seemed to me to be scams.
Even primary vendors have outsourced their recruiting to India.
(Seattle-area, if it matters, and it does.)
$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.
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.
All I see is full time jobs, no remote, and certainly no contract jobs. Germany.