"during the initial investigation" is correct and usable in written English.
You can use it to refer to the first period of an investigation, when it has just been undertaken. For example, "During the initial investigation, the detective began by interviewing witnesses."
It was during the initial investigation 33 years ago that investigators first focused on the Prince Street basement, Mr. Kelly said.
Mr. Koschman's family has contended that there was a police cover-up during the initial investigation.
He rejected suggestions that the security services had "pulled the wool" over his eyes, following concerns over how MI6 and counter-terrorism officers had handled some evidence during the initial investigation.
Records turned up during the initial investigation show that Mr. Andrews used $16,574 from his political action committee to buy four business-class plane tickets for himself, his wife and his two daughters to attend a wedding in Scotland.
But the investigators thought e-mails on the computer might include some from Clinton's first three months as Secretary of State that they had been unable to locate during the initial investigation, Comey said, and this was important because, "if there was evidence that she was acting with bad intent, that's where it would be, in the first three months".
Three people were arrested during the initial investigation but were released without charge.
Plasma was stored at −20°C and only thawed once during the initial investigations.
All eight cadets involved in the incident provided statements to the school during the course of the initial investigation.
In the verdict, the special court criticised the initial investigation and the police for "not doing any policing during the 2002 riots and then deliberately conducting poor investigations".
The initial investigation into the police was expanded to include an analysis of its municipal courts.
