“Reality is one, though wise men speak of it variously” (Rigveda).
Before going to the final conclusion, we will take a small diversion here.
If you look at your fingers, you would find that all our fingers are of different shapes and sizes. The same thing is true about the perspectives of people about a thing, especially when there is no definite proof.
Here, I am mentioning a small story.
The Story of Six Blind Men and an Elephant:
Once upon a time in a small village in India, there lived six blind men, who were blind congenitally. They were blind but were intelligent and curious. They used to listen to the stories told by others and used to imagine things how they would be.
They were curious about many things but were most curious about elephants. They used to argue how an elephant would look. As the days went on, their argument started turning into a quarrel. There was a villager who was working as a gardener at the palace of the king. With his help, the people of the village arranged a visit for them to the palace to learn the truth about elephants. The gardener led them to the elephant and let them touch it.
The first blind man touched the side of the elephant and declared, “An elephant is smooth and solid like a wall.”
The second blind man touched the limber trunk of the elephant and said, “An elephant is like a giant snake.”
The third blind man touched the pointed tusk of the elephant and announced, “An elephant is like a sharp spear.”
The fourth blind man touched one of the four legs of the elephant and said, “No, an elephant is like a pillar like a tree-trunk.”
The fifth blind man felt the moving ear of the elephant and said, “No, it is like a fan.”
The sixth blind man touched the tail of it and scoffed, “You all are fools. It is like a rope.”
After this, they all broke out into an argument again and started shouting and claiming how only each of them was correct and others were wrong.
“Stop shouting,” an angry voice erupted suddenly from nowhere. This was the king, who was disturbed by their noise.
He further continued, “An elephant is a very large animal. Each of you touched only one part of it. If you put the parts together, you would see the truth.”
We all are blind men who are quarreling over what exactly a Shiva lingam is, and we need someone to tell us the truth. Who would be a better person to tell us the truth other than Lord Shiva himself?
In the Shiva Purana, he has told us that the Shiva lingam is his formless aspect and is a pillar of fire. In the Skanda Purana, he says that the whole universe is created from linga and would dissolve into it. A pillar of fire looks golden or yellow in color. It has no beginning or end means it looks like a standing egg. All these things point toward Hiranyagarbha. That is why Banalingas are worshiped and considered more sacred than contemporary Shiva lingam because it is an unexploded cosmic egg and contains the whole universe inside it.
We have also seen that it perfectly matches with the initial singularity out of which the whole world was created and would ultimately dissolve.
Therefore, we can conclude that in the swayambhu form, the Shiva lingam is Hiranyagarbha or the initial singularity, and the contemporary form represents the story of Lingodbhava, i.e., the moment of creation in which the lingam is the cosmic egg and the yoni is the navel of the Supreme Creator, i.e., the source. This source is sometimes called Adishakti (First Supreme-energy) and hence associated with Goddess Parvati.
If you do not want to associate science with religion, then also the above assumption stands true.