Q: Can we say all mortals begin their first form of existence on Urantia and had never existed before elsewhere and will continue to other worlds like Mansion as their second stage of existence after death?
A: Yes, you are correct. We can say that this life is our first life, according to Urantia Book teachings:
39:4.13 To the inhabited worlds the quickeners of morality portray mortal life as an unbroken chain of many links. Your short sojourn on Urantia, on this sphere of mortal infancy, is only a single link, the very first in the long chain that is to stretch across universes and through the eternal ages.
And this next passage makes it clear that our "second life"—our second stage of existence—is going to be spent on the Mansion Worlds of Jerusem...in the "first heaven..."
15:7.5 Jerusem, the headquarters of your local system of Satania, has its seven worlds of transition culture, each of which is encircled by seven satellites, among which are the seven mansion worlds of morontia detention, man's first postmortal residence. As the term heaven has been used on Urantia, it has sometimes meant these seven mansion worlds, the first mansion world being denominated the first heaven, and so on to the seventh.
Nowhere in The Urantia Book are we taught that mortals enjoyed any individual existence prior to our birth on Urantia.
Thanks again for writing, and I hope that this reply has been helpful to you. Please write back anytime!