Most Protestant/evangelical sects don’t preach an “underground” church but rather a “universal” or “invisible” one comprising all people who believe directly on Christ for eternal salvation. Baptists have a long history of bitter difference with the CoC over just this kind of issue, the CoC being almost as dogmatic as the RCC about the unique power of baptism in their local houses of worship, and the Baptists saying no, salvation is based on personal relationship with Christ which in turn is based on hearing the Bible message, and baptism is a ceremony of witness. The Baptists match up with most other Protestants and evangelicals in this regard. The question of canonical Christian scripture was settled before the church got into anything which is anathema to most Protestants and evangelicals (e.g. alliance with a pagan government).
So how old is “my church”? As old as creation.
Where did you ever hear that? Don't believe everything you hear. The New Testament does not say anything about the location of baptism or the identity of the administrator making any difference. A believing penitent could get Mahmoud Ahmajinedad to baptize him in the Persian Gulf and it wouldn't make any difference to God. Of course it would make a differnce to the beliver's physical well-being if Ahmajinedad wouldn't let him up. :)
What does the Bible say in Acts 2:38?
Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins...
He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
1 Peter 3:21:
The like figure whereunto [even] baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ
Right. In your mind yes.
In history books no.