OTL there were several plans to marry off the daughters of Czar Nikolai II and Alexandra Feodorovna. Namely Olga, had been affianced unofficially first to GD Dmitri Pavlovich, Carol II of Romania, Edward VIII of Great Britain and Alexander of Serbia; Tatiana was considered for Alexander of Serbia, too (although Nikolai II had noticed that Alexander was attracted to Tatiana more than Maria). Maria and Anastasia, I have no idea for any engagements official or unofficial, but that Louis Mountbatten "Dickie", 1st Lord Mountbatten of Burma, had a crush on her.
Olga famously remarked that "her parents would not force her to marry someone she didn't like", but also that "she would like to stay in Russia and marry a Russian". Now, while this would be considered ludicrous by most dynastic standards - the fact of the matter remains that just before the birth of Anastasia Nikolaïevna, the Czar was considering changing the Pauline Succession Laws to have Olga become heiress to the throne. In which case, a marriage to the eldest son of a foreign prince would've been out, and she would've most likely jumped the broom with one of her cousins.
So, what if at least one or two of Nikolai's daughters make it out of Russia to marry abroad, or Alexei dies in 1912 (where he almost died OTL), causing Nikolai to change the laws, and declare Olga as Czarevna, and thus marry her to a Russian?