Did the Early Church Believe Baptism was for Salvation?

Yes!

The Epistle of Barnabas 11:11, between 70 and 131 AD:
“We go down into the water full of sins and pollutions; but come up again bringing forth fruit; having in our hearts fear and hope which is in Jesus Christ by the Spirit.”

Clement, Fragment from Eusebius, Book IV, chapter 62, around the close of the First Century AD:
“A Christian is one who knows God, who believes in Christ, who possesses the grace of God, and who has been dipped in the sacred laver.”

Hermas, Pastorals, Similitude ix, 16, around the beginning of the Second Century AD:
“The water in which men go down bound to death, but come up appointed unto life.”

Tertullian, On Baptism, Chapter 1, AD 155-215:
“Happy is our sacrament of water, in that, by washing away the sins of our early blindness, we are set free and admitted into eternal life!”

Council of Nicaea, AD 325:
“He who is baptized descends indeed, obnoxious to sins, and held in the corruption of slavery; but he ascends, free from the slavery of sins, a son of God, heir-- yea, co-heir-- with Christ, having put on Christ, as it is written, ‘As many of you as were baptized into Christ have put on Christ’.”