The trial had been set to start May 5, but O'Neill agreed to delay the proceedings while the defense waits for visas to allow Yandamuri's mother and brother to come from India.
Defense attorney Stephen G. Heckman said the relatives would be crucial character witnesses if the trial gets to the penalty phase, where Yandamuri could face a death sentence.
Unlike previous hearings - at which Yandamuri has attempted to dismiss his attorneys, interrupted the proceedings, and been reprimanded by the judge - Yandamuri sat quietly Thursday, occasionally writing notes or whispering to his attorney.
O'Neill also weighed arguments about whether Yandamuri's history of gambling can be used at trial.
Yandamuri had filed for bankruptcy in Nevada to resolve about $32,000 in casino debts from 2011, Heckman said.
He continued to gamble at Valley Forge Casino. Three days after the grandmother's slaying - before the baby's body had been found - detectives found Yandamuri at a blackjack table and took him in for questioning.
Prosecutors said his gambling losses would be presented as a motive for the alleged ransom attempt.
O'Neill said he would rule on that evidence at a later date.
Venna was visiting from India and babysitting her granddaughter when the kidnapping occurred. She was found stabbed to death in her son's home at the Marquis Apartments in King of Prussia.
Authorities and relatives searched for Saanvi for four days before finding her body in the basement of the apartment complex.
Yandamuri lived in the same complex and was a friend of the family, prosecutors have said.