Was Israel God's means of bringing redemption to the whole human race?

Yes. The context teaches that God's plan of redemption for the whole human race was tied to the seed of Abraham and the seed of the woman, who is Christ, and it was going to be accomplished through the nation of Israel. Peter therefore addresses Israel as the covenant people, saying God sent Jesus to bless them first.

Les explains that Acts 3:25-26 ties Peter's appeal to Israel back to Abraham and Genesis 3:15, where the seed is Christ. This was all part of God's plan of redemption for the whole human race, but it was going to come through the nation of Israel. Peter pleads with them as the children of the covenant to believe and accept Him as their King and Messiah. Verse 26 says, "Unto you first," meaning Israel first; every Jew had to believe and be converted, and then they could have had the Tribulation, the King, and the Kingdom, and could have evangelized the whole Gentile world.

Acts 3:25

Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed.

How is God's plan of redemption connected to Israel and the seed promise?

Redemption is tied to the promised seed, who is Christ—both the seed of the woman in Genesis 3:15 and the seed of Abraham through whom all kindreds of the earth would be blessed. God's covenant promise ran through Israel, the covenant people, and Peter declared that blessing was sent to them first.