Technical director Francois-Xavier Demaison and head of aerodynamics Dave Wheater both left the team in December, in parallel with the departure of former team principal Jost Capito.
While Williams moved quickly to hire Vowles from Mercedes as its new team boss, the two top technical jobs remain unfilled.
Given the gardening leave that such positions usually involve, it could be many months before the chosen candidates will be able to start work.
"I think the primary thing is we don't have the structure in place technically, obviously, as a result of the changes that were made," said Vowles when asked what his priority is.
"And number one is let's put in place a proper set of structures, in terms of technical director, head of aero. That's number one, because clearly an organisation needs those to move forward."
Vowles insisted that he is in no hurry to fill the top technical job, as he wants to get the right person.
"So there's a strong organisation in place, and it's acting without a TD," he said. "As we speak today, there's a car on track, it's built. They did an incredible job over the winter to achieve that.
"What's clear is this is not about short-term putting someone in place, this is about long-term, and making sure we have the right person in place. We're not going to rush to a decision, the key is making sure we find the person that fits the organisation for the long term."
Vowles stressed that he has found a core of passionate personnel at the team, despite its lack of success in recent years.
"There's a number of great people there on site," he said. "They've obviously had a difficult probably last 15 years or so, due to just circumstance, lack of investment and otherwise.
"But you can still tell that there the same level of passion that is shared, irrespective of the grid position you're in, is there, and available to you. And the work, whatever it takes really to move forward."
Vowles admitted that he will have to get used to working at a team that doesn't have the same resources as Mercedes.
"It's just understanding where Williams is. I had the benefit really, of being in an organisation where if you required something, you asked for it, and you're provided with it. We had everything you could possibly imagine.
"And it's a stark contrast to where I'm now. especially in an environment in the cost cap where it's difficult to request or even pay for what you need."
Vowles said it's too early to draw any conclusions about the new car despite some encouraging lap times in Bahrain.
"The wind and the direction it is in Bahrain at the moment, a tailwind into Turn 1, actually makes the balance very difficult for the drivers," he noted. "So it's a struggle as a result of that. It's quite a nasty feeling when the wind's behind you, especially under braking.
"Otherwise, I think there's some positive commentary, certainly relative to last year. But it's an early sequence of events where we are now, just two days into testing, to really draw any sensible conclusions."
