Option (A) is the correct choice:
"Waterlogged latex balls found at El Manati and representations of ballplayers painted on ceramics found at San Lorenzo attest to the fact that the Mesoamerican ballgame was well established by the mid-thirteenth century b.c."
The subject of the sentence is "waterlogged latex balls" and "representations of ballplayers," which are two separate items that both attest to the well-established nature of the Mesoamerican ballgame. Therefore, the verb "attest" should be in the plural form "attest" rather than the singular "attests."
Option (B) and (C) both use the singular verb form "attests," which is incorrect. Option (C) also changes the phrasing of the sentence by removing the word "painted" after "ceramics," which alters the meaning.
Option (D) and (E) both use the phrase "the finding of waterlogged latex balls" instead of "waterlogged latex balls found," which makes the sentence unnecessarily wordy. Option (E) also changes the phrasing by placing "of representations of ballplayers painted on ceramics at San Lorenzo" after "the finding of waterlogged latex balls at El Manati," which makes the sentence more difficult to read and understand.