I saw TV first time in 1957. Finland had no TV transmitters, so programs came from Soviet Estonia. I distinctly remember watching romantic Russian film with a catching tune. Perhaps named "Moscow Lights"?

How this is even possible that I remember all this, because I was 4 yrs old?

Gemini knows:

The Film: In the Days of the Spartakiad (1956/1957)

The song "Moscow Nights" was originally written for a documentary film called "In the Days of the Spartakiad" (V dni spartakiady), which chronicled a massive Soviet sports competition.

The Scene: In the film, there is a romantic, quiet scene where athletes are resting in the countryside near Moscow at night.

The Music: The song was sung by Vladimir Troshin. It was intended to be background music, but it was so hauntingly melodic that it became an overnight sensation across the USSR and its neighbors.

The Finnish Connection: In 1957, the song became a massive hit in Finland and Estonia. Since you were watching Estonian TV, you likely saw a version where the dialogue or narration was dubbed into Finnish—a common practice for broadcasts intended for Finnish-speaking audiences across the Gulf of Finland.