+1 get a job in the UK for a company that also employs a lot in the US then after a year try to transfer internally under an L-1 visa. Otherwise it will be very difficult.

Thanks for the feedback, the internal transfer route within a company for an electrical design engineer as I am is looking like the best option.

“What is generally the best path for securing a role in the U.S. as an engineer?”
Two letters: no.

I would be very wary with moving to the US due to the way that US engineering companies are doing right now. Lots of big random firings even in non-engineering companies.

I'm a UK-raised Mechanical Engineer who back in 1988 decided to do what you are aiming to do.
It was a LONG complicated and expensive process, but I achieved it. I'm now 63 years old and retired in the USA.
Back in 1988 I was working for Rolls-Royce Aero Engines. GE Aero Engines needed a lot of engineers and came over to the UK to poach British engineers from their competitor. I was offered a position and waited for my green card to come through. I left Rolls-Royce and took a contract position in Germany while I waited. After 18 months I was told my green card was ready, BUT GE no longer needed me. Crap. I took a few more contract positions in the UK while looking for alternative avenues. It took four years for another opportunity to present itself: a contract position in Canada working for a US corporation. After five years in Canada I Naturalized as a Canadian Citizen in 1998 and was then eligible for a TN (Trade NAFTA) visa to transfer to the same company's US operations. There followed 10 years on a precarious path to US green card and US Citizenship. At any time during those years I could have lost my job and been required to leave the USA and abandon my application. Learning how to navigtate two country's immigration systems became my second job. My company didn't help me with the immigration process, but fortunately, they did stick by me (despite me being a non-Citizen and excluded from much of their defense-related work). My UK-born wife, four UK born children and I became US Citizens in 2008. I've had a rewarding career and now have a well-funded retirement. Better still, as is the wish of every immigrant, my children are all doing even better than I.
So...all the best with fulfiling your goal. It will be very challenging and you may need to take some backward steps to move forward, but it can be done and it can be rewarding in many ways.
Mike

I am not an electrical engineer. But decided to move here to the US at age 21. It took me about another 10 years to get the education and experience needed to get the job that then moved me here on an L1a. After that I got got my LPR around a year later so I could buy ann anpoarent and propose to my then USC girlfriend. And then I waited another 5 to become a USC on my own merits. (I could have done this a little sooner on the basis of being married to a USC). The L1 is one of the smoother paths if you qualify (it’s not as simple as working for an employer for 1 year, those who think it is likely did not come via that route, many came via family route/marriage). I called my path the TYP (10 year plan) but if someone already has the required education and experience they could do it a lot faster. With the minimum being about 14 months of everything was “perfect”. I.e. job with a blanket petitioner for long term you need L1a who will sponsor LPR, L1b is not as “direct” a path.