I have found that Adam and Eve spoke Adamic language. But for that there is no X-English dictionary. Then in the Tower of Babel they said that the first one was Hebrew, which is my guess here.
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Sumerian and Egyptian are the two languages we have the oldest understandable written texts from. Which one counts as "older" is a difficult question to answer, because we can't make dictionaries based on just the oldest attested artifact for each—a lot of the information needed to really document the language comes from much later sources. Akkadian could also perhaps lay claim here; the oldest Akkadian records may be younger than the oldest Sumerian and Egyptian ones, but they're older than the bulk of the corpus needed to properly document those languages.
I have found that Adam and Eve spoke Adamic language.
Then in the Tower of Babel they said that the first one was Hebrew
Note that these beliefs are not common among modern scientific linguists. The origin of language in the first place is still a matter of much debate, but it's widely accepted that Hebrew descended from Canaanite descended from Northwest Semitic descended from Proto-Semitic descended from Proto-Afro-Asiatic.
One interpretation of the question is, what was the first language X for which there is an X-English dictionary? The dictionary of syr Thomas Eliot knyght (1538) is probably the first such dictionary: X is Latin. For the other direction (from English to some language) the first bilingual dictionary is Promptorium parvulorum, ca 1440, which is English to Latin.