The WFAA-TV coverage video seems to be uninterrupted. The only film they had of Oswald before the 3:30 time of CBS's film was from the Texas Theater. And it didn't show enough of Oswald for anyone to recognize. So it does appear that CBS was first. And it fits the time frame for the search at the North Beckley address.
In "With Malice" by Dale Myers (Loc 5430 on my Kindle), I found the following:
3:10 P.M. - WFAA and WBAP television in Dallas were broadcasting the first photograph of suspect Lee Harvey Oswald, take by AP photographer, Ferd Kaufman. The caption transmitted by the Associated Press, with the photograph, underscored the belief that Oswald was guilty of murdering Officer J.D. Tippit:
"Gunman kills policeman - Lee H. Oswald, 24, was arrested in Dallas today in connection with the slaying of a Dallas policeman shortly after President Kennedy was assassinated. He was also being interrogated to see if he had any connection with the slaying of the president."[814]
Footnote [614] CD723, p.2 (FBI LHM, March 30, 1964, Re: First time Oswald's picture was displayed on local Dallas television)