Assuming that the night sky is clear,
you could even be an amateur astrologer
for the stars to tell you where that new moon is.
These three diagrams almost need no further explanation.
Alignment of sun, earth and new moon:
(hermit eclipse | The Science: Lunar Months)
Zodiacal constellations are a clock-face-like celestial calendar:
(EarthSky | What is the zodiac?)
Example for January:
(Click here to keep these diagrams visible.)
Some explanation anyway:
Being an amateur astronomer,
you know that a new moon occurs when the moon is very close
to being in the direct line between sun and earth.
That is why a new moon, like the sun, is never in the night sky.
Now, being an amateur astronomer, or astrologer,
you know that the zodiacal
constellations — Aquarius, Aries, ...,
Virgo — take turns...
...aligning with sun and earth, depending on the time of year.
On any day of the year, you also know which constellation,
perhaps even which star, is in alignment and opposite the sun
as seen from earth.
So, to know where the sun is at any moment,
imagine a straight line from that opposing constellation/star to you.
Extend this line through you and the earth.
That extended line will point to the sun and thus also to the new moon.
In January, as an example, ...
...Virgo is the constellation opposite the sun form earth's perspective.
Extend the line from Virgo to you through the earth
and that line will point to the new moon.
Incidentally, you don't even have to know beforehand
about constellations or stars
if you can see the sun set or rise on the horizon
and, at the same time, ...
...if you can see which star is rising or setting
on the horizon exactly opposite the sun.
That would be the star to follow all night.
During most of January it would be in Virgo.
(This solution was posted exactly a day after an absolutely new moon,
as in solar eclipse.)