Unfortunately, much like the UK, it is very difficult to permanently bring another person over to the USA without first being married. The other options I can think of, without marriage, would be if she qualified for a visa in her own right. This would be akin to a student visa or a temporary work visa.
Of course, both of these options are only temporary and she would have to leave at the end of her visa, if not able to extend them. However, I must let you know that immigration officers will ask if she has any partners/people she knows in the USA, and could use that against you both as a means of her overstaying her welcome in the US.
This is unfortunately one of the very few ways you guys are able to do this without marriage, and even then it's not a sure-fire method if the immigration officer suspects she is doing that if her underlying reasons for traveling to the US are not study or work, but to live albeit temporary with a partner - this is cause for refusal alone.
Getting married in order to get the visa, and then divorce quickly afterwards, is clear-cut immigration fraud. If charged with this, she'd likely receive a very lengthy ban or even a permanent ban from entering the US and you could also face charges and financial penalties, as well as a criminal record. I know you have stated it's not immigration fraud per se as you state she is normally welcome in the US, but being normally welcome in the US unfortunately doesn't mean one can marry for visa purposes.
In addition, I am certain if you married and the visa was obtained, that visa would be conditional on the basis of your marriage. Meaning if you were divorced, her visa would no longer be valid. Plus, divorcing so quickly right after a visa has been granted is an instant red flag for immigration who would likely investigate this and probably arrive at a guilty verdict conclusion.
US immigration is tough and apart from the methods outlined earlier, it's very difficult to bring a partner over permanently, unless, like I stated earlier, she qualifies for another type of visa in her own right - and even this may be temporary.
All things said, if you guys do get married for visa purposes please just be aware of the consequences surrounding it if caught - they are life-changing for both of you. I won't lecture you on what not to do - that's up to you, though I won't condone it as that'd be irresponsible of me.
Finally, they will ask for a marriage certificate. Getting a spouse visa (or the equivalent to one in the USA) requires you two to actually be spouses - and unfortunately they need proof of that as peoples' word just won't do (imagine that). So they ask for a marriage certificate.
Best of luck, though. Being separate from a loved one is one of the worst things in the world but I would recommend doing it the proper, legal way without having to look over your shoulder every day wondering if ICE teams are going to come knocking.