I wanted to comment on Joshua 5:10-12, which is sometimes being used a some kind of proof that Counting of Omer begins right after Passover (on the 15th of the 1st month).
Let's take a look at it and see if it is true:
YLT Jsh 5:10 And the sons of Israel encamp in Gilgal, and make the passover on the fourteenth day of the month, at evening, in the plains of Jericho;
YLT Jsh 5:11 and they eat of the old corn of the land on the morrow of the passover, unleavened things and roasted corn, in this self-same day;
YLT Jsh 5:12 and the manna doth cease on the morrow in their eating of the old corn of the land, and there hath been no more manna to the sons of Israel, and they eat of the increase of the land of Canaan in that year.
As you can clearly see from the first verse (5:10), ALL Children of Israel were at Gilgal, which means they were all in one place. What does this mean? Very simple! It means that obviously it was possible for them to bring in the Wave Sheaf on the 15th, as this was "old corn" of the land. This was not Wave Sheaf of the grain that was sown, but rather a Wave Sheaf of the grain of the land that was already there and was self-grown.
In other words, since Children of Israel were in one place, there was no difference in harvest time. All of them brought a Wave Sheaf as required and at the same time. Normally, once Children of Israel have settled throughout the land, the average harvest time would be at least a week later, which means that the High Priest would announce the Counting of Omer later, probably as early as right after Passover week.
I am saying all this, assuming the book of Joshua makes any sense and is accurate. Technically speaking, Book of Joshua is not Written Torah, so we do not have to explain it or use it to interpret the Written Torah. I was providing this explanation purely because it made sense to me, and because traditional explanation was clearly wrong.
So, if you will look at my calendar, you will see that the EARLIEST the Counting of Omer could start was the last Shabbat of Passover.
Once again, the High Priest would determine the day of the Wave Sheaf and Counting of Omer.
I hope this clarifies this matter.