I translate Baha'i a little differently I consider it 'the follower of the Glory or the light,' and not the follower of the person. I believe the 'first' can be interpreted in different ways, but nonetheless it is not a meaningful question, since of course, Christ is the Manifestation of God for Christianity, Muhammad is the Manifestation of God for Islam, and Baha'u'llah is the Manifestation of God for the Baha'i Faith.
@paarsurrey is playing rhetorical word games with no meaning. The valid question is whether Christ, Muhammad, and Baha'u'llah are who they claim to be.
We could say the Bab was the first Baha'i, after all that Message was to prepare the way for all to accept Baha'u'llah.
But as you suggested, names are a barrier to seeing the one source of light. I would say it is not wrong to say that the person of Baha'u'llah being the mirror of that light, is the First to be that light in the age it dawned and the first to live by that light.