you didn't take into account the Greeks who did have contact with the Romans, who were in contact with the indians and it is believed by some that a Buddhist monastic group existed in Alexandria (?) and words such as Therapy are thought by some to of originated from this group (Christopher Titmus has written an article on this). The Greeks did have contact with Egypt as well which is one place it is thought that jesus went, then there is also the evidence that St Thomas the apostle (Gospel of Thomas fame) is believed to of, and evidence exists for this, went to India where a church group existed for about 1500 years before it was brought into the roman churches fold.
Although I do not believe that jesus went to india and the historical accuracy of the bible is unlikely the contact between the cultures and the small amount of common ground maybe coincidental but may not be for a variety of reasons.
Those who have said the Buddha or Jesus didn't exist I would like to see them prove Shakespeare did exist! there is very little evidence that Shakespeare as an actual
person did exist and some have put forward that he was a pseudonym of a group of or one writer(s) who weren't getting their plays produced so made him up spread rumours about how good his plays were etc
He who knows only his own side of the case knows little of that. His reasons may be good, and no one may have been able to refute them.
But if he is equally unable to refute the reasons on the opposite side, if he does not so much as know what they are, he has no ground for preferring either opinion …
He must be able to hear them from persons who actually believe them … he must know them in their most plausible and persuasive form.