Applying to U.S. Embassies and Consulates

Unfortunately, trying to apply for a visa through US consulates seems like an illusion.

Yes, theoretically this method still exists. Despite the fact that the United States Embassy in Kyiv has completely suspended work, Ukrainians have the opportunity to contact embassies and consulates located in neighboring countries, for example, in Poland (by the way, all the staff of the diplomatic mission was moved to Poland). But the process of reviewing documents for the provision of American visas over the past year has been very slow due to covid-19. And now the queues can stretch for years. Still, it's worth trying!
If the visa application has already been sent to the US Consulate in Kiev, then you should contact the US consulates in other countries and ask to transfer your case to them.
In the case where the petition for a visa has been approved by the immigration service, you should apply to the US National Visa Center, providing data on the case number and its details.
Applying for political asylum at the US border

Another option for settling in the States is to arrive in a country bordering the United States (i.e. Canada or Mexico) and then apply for refugee status (asylum) at the border crossing.

The US government grants this status to those who cannot return to their home country due to imminent persecution in their home country.

Obtaining Temporary Protected Status
This program covers persons who cannot safely return to their country. Now such a status can be obtained, for example, by citizens of Somalia, South Sudan, Syria, Haiti, Yemen. But it is expected that in the near future the list will be replenished with Ukraine. This is a temporary measure that does not confer legal permanent resident status or any other immigration status, but the applicant may still be eligible to work in the States as well as receive immigration benefits.

Yes, each situation is individual, but! I hope to explain to you that everything is real, you just need to want to!