The New Testament and the Sacraments

Does the New Testament teach the Sacraments? Some would argue that sometime after the apostles died, the Church 'invented' the idea of Sacrament, esp. in the Medieval era.

Consider, though, the book of John. Call it the 'secret Sacramental' gospel with multiple allusions to baptism and Eucharist. For example:
John 2, Jesus turns water into wine.
John 3, no one can see the Kingdom unless they are 'born of water and the Spirit.' At the end of John 3 we see the only place where Jesus' disciples baptize.
John 4, Jesus offers the woman at the well 'living water.'
John 5, the man is healed before entering the waters of the pool of Bethzada.
And of course John 6 Jesus calls himself the 'Bread of Life' and says, 'unless you eat my flesh and drink my blood you have no life in you.'

I find the data fascinating. We need to remember there was a Christian community that coexisted with the writing of the New Testament--a community that was presumably sacramental.