Lutheran here. I'll say something which will probably confuse and enlighten things: I believe that baptism saves... by faith alone. Calvinists tend to see baptism as a symbolic covenant seal, while Lutherans see it as an actual, supernatural working of God (aka a "miracle") to deliver the forgiveness of sins to those who believe (or "the elect" if you prefer). If you believe in monergistic salvation, it makes sense that there should be a specific point in time where God supernaturally creates saving faith in you. Luther argued that this happens in the waters of baptism, since the Word of God is present there with the water

Here's the big kicker: pretty much all of this depends on what you believe concerning irresistible grace. Luther wanted to make it clear that although the action of baptism really does offer miraculous power, that power is only received by faith. In other words, Luther saw no contradiction between baptismal regeneration and Sola Fide. Baptism regenerates, but only for those who believe

Side note: I'm enrolled at a Lutheran pietist seminary and am therefore knee-deep in the tension between the objective reality of God's saving work and the subjective experience of us converting. I'm starting my 3rd Systematic theology course in a few weeks, so I should be able to weigh in on this more after I finish that up