The Verdict: Need More Info
This turns on how your family came to hold Soviet or another citizenship when the border moved. Apply for a decision confirming whether they kept Polish citizenship, and look at the Karta Polaka route meanwhile.
Under article 4 of the 1951 Act, a Polish citizen of 1939 living outside Poland in January 1951 was not treated as Polish if they took another citizenship under a border agreement, or were of Ukrainian, Belarusian, Russian, Lithuanian, Latvian, Estonian or German nationality. That loss cannot be undone by restoration.
The voivode decides on a confirmation application whether article 4 actually applied. Prewar Polish documents, and records of how and when the family received Soviet papers, are the evidence.
Whatever that decision says, our diaspora route is likely to work: a Karta Polaka or proof of Polish origin gives permanent residence in Poland and citizenship a year later. If the family lived in Kazakhstan or another Asian part of the former USSR before 2001, look at our historical displacement route too.