Embodied said: “that there’s something of my gandhabba in yours and vice-versa?”
Why do you need to make things so complicated? What does it have to do with a beginning? Please think carefully and formulate your question correctly. I am still not sure what your question is.
How can two gandhabbas overlap? Gandhabba is a lifestream, just like a brahma. The only difference in a human is that we have physical body with the gandhabba inside. A brahma only has a gandhabba or a mental body.
Embodied said: “But once achieved isn’t Nibbana an Absolute knowing?”
First think about “knowing”: That involves “thinking”. Thinking involves thoughts which means citta and cetasika. Those belong to this world of 31 realms.
Everything in the 31 realms have citta, cetasika, rupa (matter). Nibbana does not have ANY of those. It is useless to speculate what is in Nibbana.
We don’t know ANYTHING AT ALL about what is in Nibbana. All we know is that Nibbana exists and that it is OUTSIDE the 31 realms; see the posts in “Nibbana“.
I don’t have any idea how the initial question on “no discernible beginning” is connected to different Buddhas etc. Please formulate your questions carefully. It is a waste of time to try to understand what is meant in a question.
Please read about Nibbana before asking any more questions: “Nibbana“.
P.S. There is nothing special about a gandhabba. Any living being has a mental body or manomaya kaya. For a human or an animal, it is given a special name of gandhabba.
The manomaya kaya keep changing as one goes from bhava to bhava. In some brahma bhava, it is the only body. In other bhava there is a denser body associated with it.
If question is whether there was a first bhava in any realm, then it leads to the question: How did that manomaya kaya arise? For any living being, the Buddha did not see such a first.
A related question is: If there an infinite number beings at some earlier time, and there have been an infinite number of Buddhas who helped an infinite number of living beings to attain Nibbana, how come there are still an infinite number of beings left now? Modern mathematics confirms that infinity minus infinity is still infinity!
See: “Infinity – How Big Is It?“