Lady Speedbird
From what you’ve written, I’m not certain I’ve explained myself clearly. You said you don’t want to downgrade. As it stands now, you will almost certainly be a narrowbody FO if you come to the US. You may get lucky and secure a 767 or A330/777 slot in class, but I wouldn’t count on it. Your previous experience will NOT be a factor in your initial aircraft/base assignment. That will be based on your seniority within your particular class. Typically (but not always), that’s determined by age (eldest is most senior).
If you don’t want to fly an Airbus, Delta plans to be an all-Airbus WB fleet in the future.
As someone else pointed out, you’ll go through a full type rating course when you get here, even if you got very lucky and got the 777 at United.
Also, you’ll need 1000hrs as SIC at a part 121 carrier before you can be a captain. I’m not sure if they’ve relaxed that rule to allow your previous time to count, but when last I checked (5+ years ago), this was not the case, so you’ll have to sit in the right seat for a minimum of 1000hrs before you can be a CA.
Right (or left) seat in the 757 won’t get you to the 777 any faster. It’s all a matter of seniority. You could theoretically go from 320 FO to 777 CA. Nothing would prevent that.
For now, United is offering 737 CA slots in newhire class. I’m told in one of the more recent classes, nobody wanted it, so the junior few people got stuck with it. Given you haven’t got any 121 SIC time, I’m not even certain you’d be eligible for that. Along those lines, if being a captain ASAP is important, you may want to bid NB FO instead of WB FO, as you only get flight time credit for the time spent in the seat. (Pay and rest/duty limits are based on the entire flight time though).
The last thing I’ll add is that I hope money isn’t the sole factor you’re considering. Things are good now. They weren’t always like this, and history doesn’t repeat, but it rhymes.