No minimum amount is mentioned in the Mishna or Talmud - however it must be visible. What that amount is is a scientific question, but seemingly one with no practical halachic implications, as if anyone can see it it must be visible!
However, the Brisker Rav, Shemos 12:2 writes that knowing the time of minimum human visibility does have a practical ramification, in the case where Rosh Chodesh is being calculated. Since:
- technically the moon begins to get bigger one second after the molad/conjunction,
- physical seeing is anyway not being relied upon here,
One might assume that this knowledge is good enough, and a calculated new month would be able to start any time from the calculated molad. However this is not so, contends the Brisker Rav - even in this case enough time must elapsed for it to be visible to the naked eye, despite not needing any witnesses or testimony.
As such, it is necessary to know the minimum amount of time needed. This is difficult to know, and indeed the Brisker Rav writes that this is what Rashi Shemos 12:2 means by:
Moshe found it difficult to understand the birth of the new moon, when it is visible and able to be sanctified. HKBH had to show him and say "like this - see and sanctify!"
Rosh Hashana 20b seems to indicate the time needed is 6 hours. This is also indicated by our calendar (based on the above argument), which allows Rosh Chodesh to fall on the day of the molad provided it is before mid-day.
The Ba'al Hamaor there says at least 24 hours are required for sighting, and he reinterprets the Gemara and the midday requirement to conform with this.
From the discussion in the Talmud we see another ramification - if not enough time has elapsed Beis Din would be able to reject the witnesses as liars.
