Pulliam, 38, played Cosby’s daughter Rudy on The Cosby Show.
At least one other member of Cosby’s television family — actress Phylicia Rashad, 68, who played his wife on The Cosby Show — is expected to make an appearance during the trial, says Andrew Wyatt, Cosby’s spokesman.
“I came to support [Cosby] because this is where you hear the facts. This is where the truth happens,” she told reporters, according to E!. “Ultimately, it’s easy to support someone and to be in their corner when things are great. When things are good. But…true family, friendship, integrity is how people show up and support when things aren’t looking so great, when they aren’t shining.”
Johnny Taylor, president of the Thurgood Marshall College Fund, will also show up at the courthouse, Wyatt tells PEOPLE.
Representatives for Rashad and Taylor could not immediately be reached for comment.
“Johnny feels Mr. Cosby has done so much for historically black colleges over his career and it’s important for him to show that support and say ‘Thank you’ because he has not been found guilty of anything,” Wyatt says.
“They’re coming in to hear the truth. Keshia feels the same way. She’s not here to proclaim guilt or innocence. She’s here to finally hear the truth for herself in the courtroom. She wants people to stop listening to the sensationalism and come hear the truth.”
Their appearances are all part of a public relations blitz Cosby has been on in recent weeks as his trial begins. He is accused of drugging and sexually assaulting former Temple University employee Andrea Constand in 2004 in his Elkins Park, Pennsylvania, mansion.
Cosby, 79, has done interviews with the NNPA Newswire and CNN as well as radio show host Michael Smerconish. Evin Cosby, one of his four daughters, wrote an essay defending her dad.
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The recent media blitz, plus the star power in court to support him, could have an impact on the jury, which is being brought in from Pittsburgh and consists of 10 white people and two black people, says one crisis management expert.
“The goal is to ensure that at least one or two jurors who hear Cosby’s trial will remember the good side of the man when they pass judgment,” Gene Grabowski, a partner at Kglobal, a Washington, D.C.-based public affairs firm, tells PEOPLE. “This strategy is proven to have worked. Even in murder trials, it can lead juries to impose life sentences rather than the death penalty. In many cases, it can lead to hung juries, mistrials and even acquittal.”
It has another purpose as well, Grabowski says.
“Regardless of the trial’s outcome, the goal of Cosby’s crisis managers is to ensure his legacy is at least partially preserved,” he says. “As President Trump is demonstrating, everyone — including Bill Cosby — has a base of supportive people who only need a few examples to buttress their favorable opinion of people they want to like.”
Pulliam and Rashad previously have made public comments supporting the comedian.
“I can only speak to the great man that I know and love, who has been so generous, who has been such a philanthropist, giving back millions of dollars to education and schools,” Pulliam told Access Hollywood Live in January 2015.
Cosby has pleaded not guilty to three counts of aggravated sexual assault in the case brought by Constand. He denies similar allegations from more than 60 women. The trial is expected to last two weeks.
The Cosby Show aired from 1984 to 1992 on NBC and was one of the biggest TV hits of the 1980s.