Luca Marmorini, head of Toyota's engine department, said however that he was sure they would be in good shape for Melbourne.
"The decision (to supply Jordan) was made a little bit late for us, so that means it is a big amount of work with a lot of uncertainties," the Italian told Reuters.
"I think it will be a struggle for them and for us," he added. "We started in the middle of November needing to be ready in Melbourne with a car. So if we go there and the performance is good, it will be a fantastic technical result for our group and Eddie.
"I am sure that the car will be ready for the first race. Then we hope that it will be ready in the right way and can also be a fast car and also that we can do enough tests to get the best out of the engine."
Jordan aim to roll out an interim version of the EJ15 early next month and have two weeks of testing planned before cars and equipment have to be flown to Australia at the end of February.
"The EJ15 is essentially a development of the EJ14 with a Toyota engine installation and to the new regulations," said Jordan technical director Mark Smith.
"Once we are able to move forward from this start point, the plan is to look at a significant development mid-season.
"I would be very cautious about expectations for the first races of 2005 but I
NICE CHALLENGE
The team, short of cash and fallen on hard times since they finished third in the championship in 1999, have yet to announce who will drive for them.
"We're talking to a lot of different people," said a spokeswoman. "It's no secret that we're looking for someone who is going to attract sponsorship but there's no shortage of candidates and we are keeping our options open."
Toyota, whose own team are about to start their fourth season in Formula One, came to Jordan's rescue after they were left without an engine following Ford's decision to quit.
"Already they (Jordan) got a mock-up of the engine for preliminary assembly of the car but the D-Day for them will be the rollout of the car," said Marmorini.
"From a technical point of view it is a nice challenge and we have been really impressed with how quick and flexible they are," added the former Ferrari technician.
"I feel a big responsibility to give them what they are expecting."
Marmorini said the Jordan deal would also be beneficial for Toyota, under pressure to challenge the frontrunners after spending a fortune with little reward so far.
"We have to release a lot of information to them and in the same way we get a lot of info from them as well, so it is a positive situation," he said.