Veronika Didusenko, 26, and her son Alexander fled the Ukrainian capitol after on the morning of 25 February after being woken by air raid sirens and explosions.
At a press conference in Los Angeles on Tuesday, Ms Didusenko said she grabbed a few possessions and joined thousands of other women and children heading to neighbouring countries.
The 400kms (250 miles) journey to the border with Moldova had been fraught with danger, she said.
“There was no place where sirens would not sound, where rockets and bombs would not explode.”
Ms Didusenko, who won the Miss Ukraine pageant in 2018, travelled through several central European countries before reaching Geneva, Switzerland, 2100kms (1300 miles) away.
She then travelled to the United States, after making the “heartbreaking” decision to leave her son with family in Europe.
At a press conference with her friend, the high-profile lawyer Gloria Allred, Ms Didusenko said she wanted to highlight the humanitarian disaster unfolding to women in Ukraine on International Women’s Day.
“Right now, millions of Ukrainian children and their mothers are trembling at every sound in the subway stations and bomb shelters. Even more heartbreaking that women are giving birth in such conditions in these shelters,” Ms Didusenko said.