I just did my 2nd anniversary coming to the US... Like you, I had no credit history whatsoever...
I did a couple things that nowadays enables me to have a 790 credit score and this score has been with me since pretty much 6 months in!
First thing, I added myself to the oldest credit card of my wife - about 5 years old. Right after I opened a Discover Credit card with 500 dollars limit - they were the only ones to let me open an account myself at the time right off the bat. Sure the limit was low but in the meantime it was an account - as a point of reference my CL now with their card is 10,000
I added myself to other cards my wife had, be it Target Card or some other... I opened myself a store card as well under my name.
I let it flow for 3 months, after 3 months and seeing my score in the 740s I started churning CCs for miles... I opened 3 cards myself and my wife about 5. I added myself as AU all times in order to take advantage of her Credit Limits which were much higher than mine.
Even though you should be below 10% of credit utilization, its not a big deal if you go over it. Credit utilization ratio has no memory, so, your score may drop a lot if you max out a card for example, but once your statement comes and you pay it off it goes back up - it happened to me last summer where I went over the limit with my AMEX and my score went from 740s to 670s ... once I paid off I came back to 740s.
Also I have opened a Personal Line of Credit at a bank ... and also a HELOC diversifying my credit types.
As of now, I am sitting at 790 credit score