Should Israel have known that Jesus was their Messiah?
Yes. Israel should have known and could have known that Jesus was the Messiah, because the Old Testament prophets foretold His coming, suffering, death, burial, resurrection, and ascension. Yet they did not know or understand, and Peter says they acted through ignorance, so they rejected Him.
Les teaches that Israel should have known and could have known, yet they did not know and therefore rejected their Messiah. Peter told them they acted in ignorance, as did their rulers. The Old Testament prophets had shown that Christ would come, suffer, die, be buried, rise, and ascend, and God fulfilled all these things. Israel, however, could not understand. Because they rejected Him, they suffered catastrophe after catastrophe, but God is not through with the Jew and will still keep His covenant promises with them as a nation. Peter therefore calls Israel to repent and be converted, so their sins may be blotted out and times of refreshing come from the Lord.
And now, brethren, I wot that through ignorance ye did it, as did also your rulers.