By calculating the ratio of U-238 to Pb - 209 the age of the earth can be estimated. Is it not a possibility that non radioactive lead already there formed during the birth of earth it self alter the ratio and cause an error in the estimation?
You have exactly the right idea. The decay products are only useful in as much as we can compare a previous isotopic ratio to the current (measured) ratio. How this is done differs from dating method to dating method.
As an example, C14 dating originally came about with the idea that atmospheric and therefore living plants have a near-constant ratio that can be used as the precursor.
In the case of uranium-lead dating, the difference in chemistry between lead and uranium is key. The source material is not a random rock, but a specific mineral: zircon. Zircon forms out of materials and conditions that strongly exclude lead. Undoubtedly there would have been some Pb209 in the environment at the time of formation, but it could not deposit into the zircon matrix. Instead the presence of lead (all isotopes) is near zero. The assumption then becomes that any found within the zircon is due directly to transmutation of other elements after formation.
One needs to account for lead that was formed as lead, rather than by radioactive decay. Wikipedia has a discussion. Lead-204 is not formed by decay, so if you know the primordial distribution of the isotopes, you can compute the primordial amount of each of the others. The rest comes from decay.