We don’t know how the alien race the Doctor is from got the Time Lords' powers originally. The child was found by a rift and so possibly this race of beings was conceived and born in the Time Vortex. One got lost and fell to be found.
As the Time Lords discovered regeneration before time travel, it seems possible that what was a natural genetic mutation for the child was researched and turned into a procedure that could be carried out that first time. The first act of regeneration may then complete
It is equally possible that the process (regeneratingstandard Timelord physiology, 2 hearts, multi brain cranium, was also genetically copied from the 2nd hearttimeless child, or a by product of the Time Lord brainregeneration genes, etcand the Gallifreans where just as human as anyone from earth before going down the path of genetic manipulation.)
The fact on this is we don’t know but in respect to your question it is very possible that being conceived in the Time Vortex gives the same regeneration abilities that were then taken from the Timeless Child and it wasn't until the Gallifreans discovered time travel that they realised that fact.
If the writers of Dr Who want to really fry our brains at some point in the future the DR will regenerate as a child, lose there memory and then be lost through a rift to be discovered by Tecteun :).
