Your question spans across numerology and astrology. Both have strong backing in Jewish tradition but rather when using them in a descriptive way (to explain the past) and not to make predictions. To answer your question directly, it is "Jewish" to believe people are influenced by their birthdate although they retain much freedom to influence their fate and that specific dates/months have particular influences on the Jewish people.
Jewish numerology - gematria - works with correspondence between letters and numbers, and have been used heavily in text analysis (e.g., the Baal Haturim on the Torah). In the words of myjewishlearning "If a word’s numerical value equals that of another word, a commentator might draw a connection between these two words and the verses in which they appear and use this to prove larger conceptual conclusions."
Jewish astrology also has strong sources, for instance the belief that certain months have positive (e.g., Adar) or negative (e.g., Av) connotations, see TB Taanit 29b
Rav Pappa said: Therefore, in the case of a Jew who has litigation
with a gentile, let him avoid him in the month of Av, when the Jews’
fortune is bad, and he should make himself available in Adar, when his
fortune is good.
Another gemara (Shabbat 156a) lists the impact of being born on a certain day or at a certain hour. See there at length. However the gemara concludes that there is no influence of constellations on Israel since it can be counteracted with good deeds.
It is clear that earlier Torah sages were masters in understanding seasons and gematriot (numerology) as well as other esoteric matters (see e.g., Rabban Yoḥanan ben Zakkai in Sukkah 28a).
Nowadays though, one should not use astrology or numerology to predict the future. chabad.org describes it well
The Torah states (Deuteronomy 18:10) “There shall not be found among
you one who calculates times.” The Talmud, in the name of Rabbi Akiva,
specifically applies this prohibition to one who calculates auspicious
times, meaning that one should not make astrology a dominant influence
in one’s daily life and predictions through astrology are forbidden.
Therefore one should not use horoscopes to determine one’s future
actions, though it is permitted to do character analyses through
Finally, I checked R Yaakov Hillel's Faith and Folly which is a wonderful review of all sorts of occult practices, clearly differentiating between the permitted and the forbidden. Regarding astrology he explains (pp. 55ff) that Jews are beyond the influence of constellations, even more as their perform mitzvot and improve their bonding to God through prayer and Torah study, and quotes the Zohar that a sinner severs his bond with God and his evil deeds block the influences of sanctity, therefore placing him again under the rules of the constellations.
He does not list numerology as a forbidden practice directly, but forbids divining auspicious times, divining by omens and consulting mediums and oracles.
For further reading see also here.