According to Halacha what is the earliest time can you say Sefiras HaOmer each night and be Yotzei?
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Shulchan Aruch Harav (489:12) says that if one mistakenly counted the Omer after plag haminchah, he should re-count later, but without a berachah - in deference to Tosafos' opinion that plag haminchah can be considered the beginning of the night for purposes of saying Shema.
Based on this, I would venture that if the person forgot to re-count later that evening (or anytime during the following day), then this would be grounds enough to say after the fact that he was yotzei with this early counting, and to be able to continue counting the subsequent days with a berachah.