The Astronomical New Moon is on Sunday 6 January 2019 at 1.29am. The crescent will not be visible on this day.
The calculations for crescent visibility on Monday 7 January 2019 are as follows:-
Crescent age. 38 hours 43 minutes
Crescent altitude 9.38 degrees
Crescent elongation 17.36 degrees
The crescent will be easily visible with naked eye
1st Jamadil Awwal 1440AH will be on Tuesday 8 January 2019