Well, first, English is an analytical language and Russian is a synthetic language just as Hungarian and Latin are; therefore, English doesn't deal too much with grammatical cases. Most grammatical cases in English exist in the pronominal system (system of pronouns) called the English pronominal declension. The pronouns are usually categorized into four or five categories and I'm going to include the possessive adjectives into the affray despite their not technically being pronouns because they decline as well. Let's look at the following cases for instance: (I exclude the reflexive pronouns, i.e. "myself, himself, etc.)
Nominative / Accusative / Genitive Adjective / Genitive Pronoun / Dative
1st Person Singular: I / me / my / mine / (to / for) me
1st Person Plural: we / us / our / ours / (to / for) us
2nd Person Singular (Modern): you / you / your / yours / (to / for)
2nd Person Plural (Modern): you / you / your / yours / (to / for) you
2nd Person Singular (Archaic): thou / thee / thy (thine) / thine / (to
/ for) thee
2nd Person Plural (Archaic): ye / you / your / yours / (to / for) you
3rd Person Singular (m.): he / him / his / his / (to / for) him
3rd Person Singular (f.): she / her / her / hers / (to / for) her
3rd Person Singular (n.): it / it / its / its / (to / for) it
3rd Person Plural: they / them / their / theirs / (to / for) them
Don't quote me on this because I don't know Russian and I am a little rusty on my grammatical cases, but the preposition "since" roughly translates to the preposition "from". In a synthetic language like Russian, there are "very few, if any," prepositions, so the language abounds in cases; therefore, each word will have a different form to represent the noun with a preposition attached intrinsically, i.e. the dictionary definition might be in the nominative case meaning "house", but there will be words that mean "from the house", "to the house", "at the house", "by the house", "inside the house", etc. In the case of the Russian word "отродясь", I believe this noun is declined in the ablative case if my memory should be correct. The ablative case in Latin usually corresponds to the preposition "from + noun"; I believe that's what we have here since Russian is a synthetic language. English doesn't decline nouns like that except for pronouns and the -'s suffix added to nouns to show the possessive/genitive case in English, i.e. boy's, girl's, mother's, father's, mayor's, etc.
To make a long story short, there is no word in English that means "since birth" as there is in Russian because English is an analytical language; therefore, it must use a preposition with its nouns, whereas Russian is a synthetic language; therefore, it must decline its nouns to evince parts of speech.
I hope that might have helped you out in this matter. Take care and good luck!