Having been raised in the Lutheran church, and being born again as an adult, I spent a lot of time trying to understand this question, because It never made sense to me.
It's the type of question that requires a lot of context. The first thing is to understand that Lutheranism is NOT the same as reformed, calvnist, or baptist theologies.
They have a lot of common elements, and intersections, but these old ideas about baptism point more towards Catholicism than what other reformers would teach after Luther.
Here is an excerpt from the LCMS frequently asked questions page which explains quite frankly, that while they do indeed teach baptismal regeneration, they stop short of saying that baptism is REQUIRED for salvation.
Lutherans do not believe that only those baptized as infants receive faith. Faith can also be created in a person's heart by the power of the Holy Spirit working through God's (written or spoken) Word.
Baptism should then soon follow conversion (cf. Acts 8:26-40) for the purpose of confirming and strengthening faith in accordance with God's command and promise. Depending on the situation, therefore, Lutherans baptize people of all ages from infancy to adulthood.
The LCMS does not believe that Baptism is ABSOLUTELY necessary for salvation. All true believers in the Old Testament era were saved without baptism. Mark 16:16 implies that it is not the absence of Baptism that condemns a person but the absence of faith, and there are clearly other ways of coming to faith by the power of the Holy Spirit (reading or hearing the Word of God).
Heres the link to the whole FAQ. https://www.lcms.org/about/beliefs/faqs/doctrine#baptism
This link is from the LCMS (Lutheran Church Missouri Synod). In my experience, this is about the best straight forward answers you can find. They have a bunch of stuff on baptism, and salvation in general. I think this will answer your question nicely.
With that being said,and the request for an official source being satisfied, I will give some brief points to help you contextualize the situation.
Lutherans believe human beings are saved by grace alone, through faith. They however differ from other protestants in that they believe that the sacrament of baptism, is an actually effectual means of grace, which benefits the baptized person. They talk about baptism as being "Water and the Word". So by baptism, the infant receives the word with faith.
They also teach that one can lose their salvation. Admittedly this is not brought up very much. But Lutheranism does not teach that an unbeliever, tho baptized as a child is any more saved than an unbaptized unbeliever.
By this they maintain that it is grace through faith that saves. They just do some "hand waving" and equate infant baptism with faith and grace.
As mentioned in the above quote, they do not teach that baptism is necessary for salvation.
This can all be somewhat confusing if you are coming from a Baptist/reformed understanding of things. I hope this helps!
