The former champions, last overall in 2018 with one of their worst ever showings, have been the only team whose car has yet to turn a lap.
A team spokeswoman said the FW42 car arrived at the Circuit de Catalunya at 0400 local time (0300 GMT) and mechanics were working to get it ready.
"There is still a fair amount of work to do as expected so (it is) unlikely to run until after lunch, but everyone is doing as much as they can," she added.
The first test ends on Thursday evening with four more days next week before teams pack up and ship the cars to Australia for the first race in Melbourne on March 17.
Any lack of testing time is a big setback for a team, with others such as champions Mercedes and Ferrari well into their programmes after having already completed more than 300 laps each after two days.
Williams have an all-new lineup in British rookie George Russell and Poland's Robert Kubica, returning to the starting grid for the first time since a near-fatal rally accident in 2011.
The team, who took nine constructor's titles and seven driver's crowns during their glory years between 1980 and 1997, scored only seven points from 21 races last year.
The inability to produce the car on time has raised questions about the future of technical head Paddy Lowe, who joined in 2017 from champions Mercedes and is the man ultimately responsible for delivering it.
(Editing by Peter Rutherford)
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