If you have the resources to financially support your Ukrainian refugee friends, it's possible to get them here quickly!
First hand experience: a Ukrainian friend and I just went through this process. It took us one week to get full approval. And most of that time was my gathering documents to prove my financial state. And it helped that I had copies of docs handy to prove my citizenship.
Perhaps we just got lucky, but fyi it's possible. It was free. It was all online (for us) and it was fast. I'm still stunned. Some of the other processes have estimated times of many months. And they gave no hints about how long this process might take.
NY Times Story (4/25) on the program:
https://www.nytimes.com/2022/04/25/us/politics/americans-sponsor-ukrainians.html
The Biden administration on Monday established a program that allows Americans to sponsor Ukrainian refugees and have them temporarily stay in the United States under a system known as
humanitarian parole.
The program, called Uniting for Ukraine, is a piece of a larger initiative to temporarily resettle as many as 100,000 Ukrainian refugees, but migrants themselves cannot directly apply. Instead, a sponsor in the United States must apply on their behalf, and then migrants may complete the process after their sponsor is approved