How to be jewish or come back to judaism

In Ukraine we have come through very hard period of history, many jews have been killed, too many efforts were done to erase judaism from people. like destroying synagogues, killing jews etc. antisemitism... The question is how to come back for those kids whose parents married non jewish men and women? Why did it happen? Where is our guilt or sin and how can we correct it? There are millions of such people in Ukraine.

It's actually very easy to return to Judaism and God, as they say in the Nike commercials: "Just do it!". Those whose mothers are Jewish are 100% Jewish and simply need to begin studying (online or with a local rabbi) and subsequently observing the Jewish traditions. The Soviet regime succeeded in ripping most of the Jews from their past, but it's definitely not your fault that your parents or grandparents inevitably assimilated, and it doesn't affect or harm your Jewishness whatsoever. On the other hand, if one's father isn't Jewish, that's more complicated, and such a person, if he want to be Jewish, must undergo conversion. All the best in your strive for truth and search for your roots!