Advice to travel from Mongolia to Kazakhstan

Hello! I am planing a big trip in central Asia, without taking airplanes. I will be in Mongolia in May and my plan would be to go to Kazakhstan next. I already know I will need to ask for a visa in Ulaanbaatar in advance so I can go through Russia.

My questions are, what is the fastest way to go through Russia, to go directly to Kazakhstan? Any trains or buses? How safe is it for a woman alone?

ChatGPT recommended me this itinerary:

Olgii -> Tachanta -> Altai -> Novosibirsk -> Kazakhstan

How feasible and safe is it?

I’m European, but my country is not in the EU