I work with a large engineering consulting firm, with many internationally trained persons, and my husband is almost finished retraining for electrical tech work in automation, robotics, and plc. He finally is rehired after a long work lapse, so we understand your difficulty. His last professional work was with data encryption programming for military contracts, and that ended quickly after 9-11 and the rise of DHS. To give an idea of the time.
In Canada, the first step is to have your degree accepted by the state engineering association. This should work in USA too, or you write the EIT exam. Then, become a certified EIT, just needing work experience and another exam before applying for PE status. You don't necessarily need a full P E but having an EIT status in USA with the license board shows something. . Then start looking for plc or engineering drafting work, depending on your skills. 6 mos to 1 year max is all you need to take for a couple courses at two levels for either plc or electrical drafting. Programming in general can work too. Plc work, testing, and engineering tech are decent choices if you are concerned about nationality issues with some industries.
I would say that at least half of my international colleagues choose nicknames that they like, especially asians, but pretty common across the board. I live in a diverse city. Your resume uses this name only or states Muhammed (Charles) Last name. Don't use the initial unless you really do use your middle name, as we aren't used to seeing it this way.
Previous work experience in engineering is great, especially common expat countries like UAE. If you have any.
Your largest challenge is lack of usa experience and references. That would be true if you were a Brit native with four years recent engineering work too.
. So, any decent local fulltime work, even retail would help, but try customer support or call centre for technical company or technical sales too. Even program testing or debugging works. My DH started as a program and device tester, but was quickly given plc programming and other projects at his new employment.
Good luck! It will take 3x as long to overcome the new to the country hurdles, so don't get discouraged, keep plugging. Good news is that once you are working in the industry for a couple of years, and any telephone accent is mild, you will likely have all the same Opportunities as your peers.