Demaison left at the same time as Vowles' predecessor Jost Capito last December.
"There's a strong organisation in place and it's acting without a TD as we speak today, there's a car on track, it's built, they did an incredible job over the winter to achieve that," Vowles told reporters during testing in Bahrain.
"What's clear is this is not about short-term putting someone in place, it's 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."
Former Mercedes strategy head Vowles, who was making his first media appearance since joining Williams on February 20, indicated the team were also looking for a new head of aerodynamics.
Former champions Williams were last overall in 2022 but their new car has been putting in plenty of laps in testing and featuring surprisingly high on the timing screens.
American rookie Logan Sargeant (22) was second, admittedly on softer tyres than others, in Friday's morning session while teammate Alex Albon (26) was third on Thursday morning, also on soft tyres.
"We're flying," said Albon with a smile. "It's feeling good out there.
"The DNA of the car is still the same, I still feel like we've got the same characteristics but everything is a bit more compact and the extremes are less. A good platform to start on and we've got really good mileage in the car already.
"We've been able to tick off every test item we've had planned and that's always very helpful when you've only got three days of testing.
"Obviously no-one really knows what each other is doing but when we look at ourselves from last year, I think it is progress."
Vowles said there was unlikely to be a large shake-up in the previous season's order, with the top three set to be the same and Red Bull having an edge.
