I took this picture around 8 PM PDT. As you can see moon is about 4% which means that today was indeed New Moon Shabbat and the 1st of the 2nd Month.
Today is the earliest day the Counting of Omer could begin because it is the first COMPLETE Shabbat after the Feast of Unleavened and because it is close to the time of the harvest in Canaan.
Since I am not in Canaan, I am not obligated to celebrate the holiday. I still observe 1st and 50th on arbitrary Shabbats as you can see from my calendar here. Like I said in my blog, the High Priest would determine the Shabbat of the 1st of the Counting of Omer. Since there is no Tabernacle and no High Priest, we do not have to celebrate the holiday. As far as I understand, Hebrews did not observe it in the desert during the 40 years of wanderings either. This is not the call to not observe the Torah, this is just how things are. We simply can't observe the Counting of Omer at this time.
If you are in Canaan, you can probably observe it, but once again there is no High Priest so the observance will be arbitrary and not in its appointed time.
This is why it is very important to restore the Tabernacle and the Levitical Priesthood.