The custom is that the gabbai announces the time of the Molad during the course of "Bircas HaChodesh" on Shabbos Mevorchim. What is the purpose of this? The molad is anyhow not directly connected to the Rosh Chodesh of any month except Tishrei (which, ironically, has no Bircas HaChodesh at all!).
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Shaar Hakollel (26:7) writes that our "blessing of the month" is modeled on the prayer that the Sanhedrin would recite when they declared a new month, described in Maseches Sofrim 19:9. Thus, we should know the molad before we recite this prayer, just as they did.
Homiletically, R' Shalom Dovber Schneersohn (the fifth Lubavitcher Rebbe) said that the expression נכון לידע המולד קודם שמברכין החדש ("it is proper to know the molad before blessing the month") means: before "blessing" ("sanctifying") a "new way" (חָדָשׁ) in the service of Hashem, "we need to know what it was 'born' from."
Look in Ta'amei Haminhogim 433 (3) which quotes the Sha'ar Ephrayim, who seems to explain that the exact time of the molad is when the name of the new month starts.