No, just no. I am American by birth (now a US/UK national). I'm married to a Scotsman and have been here for 15 years. We have 3 children. The BIG difference is that I wanted to come here long before I met him. We met through a friend when I was on holiday.
First of all, you can't just try out living together due to visa restrictions. The immigration process is expensive and time consuming. It was a lot easier when I first moved here and even that was a fraught time.
And yy, if you go there, marry and have kids, you are making a HUGE leap of faith if you go there. If that marriage breaks down before you have permanent residency you could be looking at being removed, without your children. Child custody laws are a lot stricter there and not as automatically in favour of the mother (similarly, even as a British national now, and with our children all being dual nationals, if my marriage broke down I would not be able to just take my children off to America (not that I'd want to)).
I really cannot underestimate how much you must really want to live in LA. I love it here, love it, love it, love it. But after I had DD1, I was so homesick it was physical. I can still remember how low I felt. It's been a huge adjustment and one I looked forward to, but still immense.
You are the one doing all the work here - the move, visa, your career - for someone you don't really know. You are making yourself very vulnerable to even consider it. You will be, to great extent, as his mercy. You won't even have health insurance when you go there! He's losing nothing. He comes here on holiday.
Every time I read threads like this my blood runs cold.
I understand wanting a baby more than anything in the world. But I'd have one on my own with a sperm donor before I even thought of making a move like this.
YOu need to take a huge step back from this. TBH, if he didn't offer to come here and get married, this would be the end for me.
I don't think you can begin to understand what it's like to live there. I thought I knew and it was still a huge shock and again, I wanted to be here.